From one point on a circular route. Video lecture “Solving text problems on movement in circles and water”

The article discusses problems to help students: to practice solving skills word problems in preparation for the Unified State Exam, when learning to solve problems to create a mathematical model of real situations in all parallels of primary and high school. It presents tasks: on movement in a circle; to find the length of a moving object; to find the average speed.

I. Problems involving movement in a circle.

Circular motion problems turned out to be difficult for many schoolchildren. They are solved in almost the same way as ordinary movement problems. They also use the formula. But there is a point to which we would like to pay attention.

Task 1. A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

Solution. The speeds of the participants will be taken as X km/h and y km/h. For the first time, a motorcyclist overtook a cyclist 10 minutes later, that is, an hour after the start. Up to this point, the cyclist had been on the road for 40 minutes, that is, hours. The participants in the movement traveled the same distances, that is, y = x. Let's enter the data into the table.

Table 1

The motorcyclist then passed the cyclist a second time. This happened 30 minutes later, that is, an hour after the first overtaking. How far did they travel? A motorcyclist overtook a cyclist. This means he completed one more lap. This is the moment

which you need to pay attention to. One lap is the length of the track, it is 30 km. Let's create another table.

table 2

We get the second equation: y - x = 30. We have a system of equations: In the answer we indicate the speed of the motorcyclist.

Answer: 80 km/h.

Tasks (independently).

I.1.1. A cyclist left point “A” of the circular route, and 40 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 36 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 36 km. Give your answer in km/h.

I.1. 2. A cyclist left point “A” of the circular route, and 30 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

I.1. 3. A cyclist left point “A” of the circular route, and 50 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 18 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 20 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 15 km/h greater than the speed of the other?

Solution.

Picture 1

With a simultaneous start, the motorcyclist who started from “A” traveled half a lap more than the one who started from “B”. That is, 10 km. When two motorcyclists move in the same direction, the removal velocity v = -. According to the conditions of the problem, v = 15 km/h = km/min = km/min – removal speed. We find the time after which the motorcyclists reach each other for the first time.

10:= 40(min).

Answer: 40 min.

Tasks (independently).

I.2.1. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 27 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 27 km/h greater than the speed of the other?

I.2.2. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 6 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 9 km/h greater than the speed of the other?

From one point on a circular track, the length of which is 8 km, two cars started simultaneously in the same direction. The speed of the first car is 89 km/h, and 16 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

Solution.

x km/h is the speed of the second car.

(89 – x) km/h – removal speed.

8 km is the length of the circular route.

The equation.

(89 – x) = 8,

89 – x = 2 15,

Answer: 59 km/h.

Tasks (independently).

I.3.1. From one point on a circular track, the length of which is 12 km, two cars started simultaneously in the same direction. The speed of the first car is 103 km/h, and 48 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

I.3.2. From one point on a circular track, the length of which is 6 km, two cars started simultaneously in the same direction. The speed of the first car is 114 km/h, and 9 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

I.3.3. From one point on a circular track, the length of which is 20 km, two cars started simultaneously in the same direction. The speed of the first car is 105 km/h, and 48 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

I.3.4. From one point on a circular track, the length of which is 9 km, two cars started simultaneously in the same direction. The speed of the first car is 93 km/h, and 15 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

The clock with hands shows 8 hours 00 minutes. In how many minutes will the minute hand line up with the hour hand for the fourth time?

Solution. We assume that we are not solving the problem experimentally.

In one hour, the minute hand travels one circle, and the hour hand travels one circle. Let their speeds be 1 (laps per hour) and Start - at 8.00. Let's find the time it takes for the minute hand to catch up with the hour hand for the first time.

The minute hand will move further, so we get the equation

This means that for the first time the arrows will align through

Let the arrows align for the second time after time z. The minute hand will travel a distance of 1·z, and the hour hand will travel one circle more. Let's write the equation:

Having solved it, we get that .

So, through the arrows they will align for the second time, after another - for the third time, and after another - for the fourth time.

Therefore, if the start was at 8.00, then for the fourth time the hands will align through

4h = 60 * 4 min = 240 min.

Answer: 240 minutes.

Tasks (independently).

I.4.1.The clock with hands shows 4 hours 45 minutes. In how many minutes will the minute hand line up with the hour hand for the seventh time?

I.4.2. The clock with hands shows 2 o'clock exactly. In how many minutes will the minute hand line up with the hour hand for the tenth time?

I.4.3. The clock with hands shows 8 hours 20 minutes. In how many minutes will the minute hand line up with the hour hand for the fourth time? fourth

II. Problems to find the length of a moving object.

A train, moving uniformly at a speed of 80 km/h, passes a roadside pole in 36 s. Find the length of the train in meters.

Solution. Since the speed of the train is indicated in hours, we will convert the seconds to hours.

1) 36 sec =

2) find the length of the train in kilometers.

80·

Answer: 800m.

Tasks (independently).

II.2. A train, moving uniformly at a speed of 60 km/h, passes a roadside pole in 69 s. Find the length of the train in meters. Answer: 1150m.

II.3. A train, moving uniformly at a speed of 60 km/h, passes a forest belt 200 m long in 1 min 21 s. Find the length of the train in meters. Answer: 1150m.

III. Medium speed problems.

On a math exam, you may encounter a problem about finding the average speed. We must remember that the average speed is not equal to the arithmetic mean of the speeds. The average speed is found using a special formula:

If there were two sections of the path, then .

The distance between the two villages is 18 km. A cyclist traveled from one village to another for 2 hours, and returned along the same road for 3 hours. What is the average speed of the cyclist along the entire route?

Solution:

2 hours + 3 hours = 5 hours - spent on the entire movement,

.

The tourist walked at a speed of 4 km/h, then for exactly the same time at a speed of 5 km/h. What is the average speed of the tourist along the entire route?

Let the tourist walk t h at a speed of 4 km/h and t h at a speed of 5 km/h. Then in 2t hours he covered 4t + 5t = 9t (km). The average speed of a tourist is = 4.5 (km/h).

Answer: 4.5 km/h.

We note that the average speed of the tourist turned out to be equal to the arithmetic mean of the two given speeds. You can verify that if the travel time on two sections of the route is the same, then the average speed of movement is equal to the arithmetic mean of the two given speeds. To do this, let us solve the same problem in general form.

The tourist walked at a speed of km/h, then for exactly the same time at a speed of km/h. What is the average speed of the tourist along the entire route?

Let the tourist walk t h at a speed of km/h and t h at a speed of km/h. Then in 2t hours he traveled t + t = t (km). The average speed of a tourist is

= (km/h).

The car covered some distance uphill at a speed of 42 km/h, and downhill at a speed of 56 km/h.

.

The average speed of movement is 2 s: (km/h).

Answer: 48 km/h.

The car covered some distance uphill at a speed of km/h, and down the mountain at a speed of km/h.

What is the average speed of the car along the entire route?

Let the length of the path section be s km. Then the car traveled 2 s km in both directions, spending the entire journey .

The average speed of movement is 2 s: (km/h).

Answer: km/h.

Consider a problem in which the average speed is given, and one of the speeds needs to be determined. Application of the equation will be required.

The cyclist was traveling uphill at a speed of 10 km/h, and down the mountain at some other constant speed. As he calculated, the average speed was 12 km/h.

.

III.2. Half the time spent on the road, the car was traveling at a speed of 60 km/h, and the second half of the time at a speed of 46 km/h. Find the average speed of the car along the entire journey.

III.3. On the way from one village to another, the car walked for some time at a speed of 60 km/h, then for exactly the same time at a speed of 40 km/h, then for exactly the same time at a speed equal to the average speed on the first two sections of the route . What is the average speed of travel along the entire route from one village to another?

III.4. A cyclist travels from home to work with average speed 10 km/h, and back at an average speed of 15 km/h, since the road goes slightly downhill. Find the average speed of the cyclist all the way from home to work and back.

III.5. A car traveled from point A to point B empty at a constant speed, and returned along the same road with a load at a speed of 60 km/h. At what speed was he driving empty if the average speed was 70 km/h?

III.6. The car drove for the first 100 km at a speed of 50 km/h, for the next 120 km at a speed of 90 km/h, and then for 120 km at a speed of 100 km/h. Find the average speed of the car along the entire journey.

III.7. The car drove for the first 100 km at a speed of 50 km/h, the next 140 km at a speed of 80 km/h, and then 150 km at a speed of 120 km/h. Find the average speed of the car along the entire journey.

III.8. The car drove for the first 150 km at a speed of 50 km/h, for the next 130 km at a speed of 60 km/h, and then for 120 km at a speed of 80 km/h. Find the average speed of the car along the entire journey.

III. 9. The car drove for the first 140 km at a speed of 70 km/h, the next 120 km at a speed of 80 km/h, and then 180 km at a speed of 120 km/h. Find the average speed of the car along the entire journey.

1. Two cars left point A to point B at the same time. The first one drove at a constant speed all the way. The second car traveled the first half of the journey at a speed lower than the speed of the first by 15 km/h, and the second half of the journey at a speed of 90 km/h, as a result of which it arrived at point B at the same time as the first car. Find the speed of the first car if it is known to be greater than 54 km/h. Give your answer in km/h.

2. A train, moving uniformly at a speed of 60 km/h, passes a forest belt, the length of which is 400 meters, in 1 minute. Find the length of the train in meters.

3. The distance between cities A and B is 435 km. The first car drove from city A to city B at a speed of 60 km/h, and an hour after that the second car drove towards it at a speed of 65 km/h. At what distance from city A will the cars meet? Give your answer in kilometers.

4. A freight train and a passenger train travel along two parallel railway tracks in the same direction at speeds of 40 km/h and 100 km/h, respectively. The length of a freight train is 750 m. Find the length of a passenger train if the time it takes to pass the freight train is 1 minute.

5. A train, moving uniformly at a speed of 63 km/h, passes a pedestrian walking in the same direction parallel to the tracks at a speed of 3 km/h in 57 seconds. Find the length of the train in meters.

6. Solving motion problems.

7. The road between points A and B consists of ascent and descent, and its length is 8 km. The pedestrian walked from A to B in 2 hours 45 minutes. The time it took to descend was 1 hour and 15 minutes. At what speed did the pedestrian walk downhill if his speed on the uphill is 2 km/h less than the speed on the downhill? Express your answer in km/h.

8. The car traveled from the city to the village in 3 hours. If he increased his speed by 25 km/h, he would spend 1 hour less on this journey. How many kilometers is the distance from the city to the village?

http://youtu.be/x64JkS0XcrU

9. Ski competitions take place on a circular track. The first skier completes one lap for 2 minutes faster than second and an hour later he is ahead of the second by exactly one lap. How many minutes does it take the second skier to complete one lap?

10. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 6 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 18 km/h greater than the speed of the other?

Movement problems from Anna Denisova. Website http://easy-physics.ru/

11. Video lecture. 11 movement problems.

1. A cyclist travels 500 m less every minute than a motorcyclist, so he spends 2 hours more on a journey of 120 km. Find the speeds of the cyclist and motorcyclist.

2. A motorcyclist stopped to refuel for 12 minutes. After that, increasing the speed by 15 km/h, he caught up Lost time at a distance of 60 km. How fast was he moving after stopping?

3. Two motorcyclists set off simultaneously towards each other from points A and B, the distance between which is 600 km. While the first one covers 250 km, the second one manages to cover 200 km. Find the speed of motorcyclists if the first one arrives in B three hours earlier than the second one in A.

4. The plane was flying at a speed of 220 km/h. When he had 385 km less to fly than he had already covered, the plane increased its speed to 330 km/h. The average speed of the aircraft along the entire route turned out to be 250 km/h. How far did the plane fly before its speed increased?

5. By railway the distance from A to B is 88 km, by water it increases to 108 km. The train from A leaves 1 hour later than the ship and arrives at B 15 minutes earlier. Find the average speed of the train, if it is known that it is 40 km/h greater than the average speed of the ship.

6. Two cyclists left two places 270 km apart and are traveling towards each other. The second travels 1.5 km less per hour than the first, and meets him after as many hours as the first travels in kilometers per hour. Determine the speed of each cyclist.

7. Two trains depart from points A and B towards each other. If the train from A leaves two hours earlier than the train from B, then they will meet halfway. If they leave at the same time, then after two hours the distance between them will be 0.25 of the distance between points A and B. How many hours does each train take to complete the entire journey?

8. The train passed a man standing motionless on the platform in 6 s, and past a platform 150 m long in 15 s. Find the speed of the train and its length.

9. A train 1 km long passed the pole in 1 minute, and through the tunnel (from the entrance of the locomotive to the exit of the last car) at the same speed in 3 minutes. What is the length of the tunnel (in km)?

10. Freight and fast trains departed simultaneously from stations A and B, the distance between which is 75 km, and met half an hour later. The freight train arrived at B 25 minutes later than the fast train at A. What is the speed of each train?

11. Piers A and B are located on a river whose current speed in this section is 4 km/h. A boat travels from A to B and back without stopping at an average speed of 6 km/h. Find the boat's own speed.

12. Video lecture. 8 problems for moving in a circle

12. Two points move uniformly and in the same direction along a circle 60 m long. One of them makes a full revolution 5 seconds faster than the other. In this case, the points coincide every time after 1 minute. Find the speeds of the points.

13. How much time passes between two consecutive coincidences of the hour and minute hands on a watch dial?

14. Two runners start from one point on the stadium ring track, and the third - from a diametrically opposite point at the same time as them in the same direction. After running three laps, the third runner caught up with the second. Two and a half minutes later, the first runner caught up with the third. How many laps per minute does the second runner run if the first one overtakes him once every 6 minutes?

15. Three racers start simultaneously from one point on a track shaped like a circle and ride in the same direction at constant speeds. The first rider overtook the second for the first time, making his fifth lap, at a point diametrically opposite to the start, and half an hour after that he overtook the third rider for the second time, not counting the start. The second rider caught up with the third for the first time three hours after the start. How many laps per hour does the first driver make if the second driver completes the lap in at least 20 minutes?

16. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 14 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 21 km/h greater than the speed of the other?

17. A cyclist left point A of the circular route, and 30 minutes later a motorcyclist followed him. In 10 minutes. after leaving, he caught up with the cyclist for the first time, and 30 minutes later he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

18. A clock with hands shows 3 o’clock exactly. In how many minutes will the minute hand line up with the hour hand for the ninth time?

18.1 Two riders race. They will have to drive 60 laps along a 3 km long ring track. Both riders started at the same time, and the first one reached the finish line 10 minutes earlier than the second one. What was the average speed of the second driver, if it is known that the first driver overtook the second driver for the first time in 15 minutes?

13. Video lecture. 6 problems for moving on water.

19. Cities A and B are located on the banks of a river, with city B downstream. At 9 o'clock in the morning a raft leaves from city A to city B. At the same moment, a boat departs from B to A and meets the raft 5 hours later. Having reached city A, the boat turns back and sails to B at the same time as the raft. Will the boat and raft have time to arrive in city B by nine o'clock in the evening of the same day?

20. A motor boat left from point A to point B against the flow of the river. On the way, the engine broke down, and while it took 20 minutes to repair it, the boat was carried down the river. Determine how much later the boat arrived at point B, if the journey from A to B usually takes one and a half times longer than from B to A?

21. Cities A and B are located on the banks of a river, with city A downstream. From these cities two boats leave at the same time towards each other and meet in the middle between the cities. After the meeting, the boats continue their journey, and, having reached cities A and B, respectively, turn around and meet again at a distance of 20 km from the place of the first meeting. If the boats initially swam against the current, then the boat that left A would catch up with the boat that left B, 150 km from B. Find the distance between the cities.

22. Two steamships, the speed of which is the same in still water, depart from two piers: the first from A downstream, the second from B upstream. Each ship stays at its destination for 45 minutes and returns. If the steamships depart simultaneously from their starting points, then they meet at point K, which is twice closer to A than to B. If the first steamship departs from A 1 hour later than the second one departs from B, then on the way back the steamships meet 20 km from A. If the first steamboat leaves from A 30 minutes earlier than the second from B, then on the way back they meet 5 km above K. Find the speed of the river and the time it takes the second steamboat to reach from A to TO.

23. A raft set off from point A to point B, located downstream of the river. At the same time, a boat came out to meet him from point B. Having met the raft, the boat immediately turned and sailed back. How far from A to B will the raft travel by the time the boat returns to point B, if the speed of the boat in still water is four times the speed of the current?

24. Piers A and B are located on a river whose current speed in this section is 4 km/h. A boat travels from A to B and back at an average speed of 6 km/h. Find the boat's own speed.

Lesson type: repeating and generalizing lesson.

Lesson objectives:

  • educational
  • – repeat solution methods various types word problems for movement
  • developing
  • – develop students’ speech through enriching and complicating its vocabulary, develop students’ thinking through the ability to analyze, generalize and systematize material
  • educational
  • – formation of a humane attitude among students towards participants educational process

Lesson equipment:

  • interactive board;
  • envelopes with assignments, thematic control cards, consultant cards.

Lesson structure.

Main stages of the lesson

Tasks to be solved at this stage

Organizing time, introductory part
  • creating a friendly atmosphere in the classroom
  • set students up for productive work
  • identify absentees
  • check students' readiness for the lesson
Preparing students for active work (repetition)
  • test students’ knowledge on the topic: “Solving word problems of various types on movement”
  • implementation of the development of speech and thinking of responding students
  • development of analytical and critical thinking of students through commenting on classmates’ answers
  • organize educational activities of the whole class during the response of students called to the board
Stage of generalization and systematization of the studied material (work in groups)
  • test students’ ability to solve problems of various types of movement,
  • to form knowledge among students, reflected in the form of ideas and theories, the transition from particular ideas to broader generalizations
  • carry out the formation of moral relations of students towards participants in the educational process (during group work)
Examination doing the work, adjustment (if necessary)
  • check the execution of data for groups of tasks (their correctness)
  • continue to develop in students the ability to analyze, highlight the main thing, build analogies, generalize and systematize
  • develop discussion skills
Summing up the lesson. Analysis homework
  • inform students about homework, explain how to complete it
  • motivate the need and obligation to do homework
  • summarize the lesson

Forms of organization of students’ cognitive activity:

  • frontal form of cognitive activity - at stages II, IY, Y.
  • group form of cognitive activity - at stage III.

Teaching methods: verbal, visual, practical, explanatory - illustrative, reproductive, partially - search, analytical, comparative, generalizing, traductive.

During the classes

I. Organizational moment, introductory part.

The teacher announces the topic of the lesson, the objectives of the lesson and the main points of the lesson. Checks the class's readiness for work.

II. Preparing students for active work (repetition)

Answer the questions.

  1. What kind of motion is called uniform (movement at a constant speed).
  2. What is the formula for the path with uniform motion ( S = Vt).
  3. From this formula, express the speed and time.
  4. Specify units of measurement.
  5. Conversion of speed units

III. Stage of generalization and systematization of the studied material (work in groups)

The whole class is divided into groups (5-6 people per group). It is advisable to have students in the same group different levels preparation. Among them, a group leader (the strongest student) is appointed, who will lead the work of the group.

All groups receive envelopes with assignments (they are the same for all groups), consultant cards (for weak students) and thematic control sheets. In the thematic control sheets, the group leader gives grades to each student in the group for each task and notes the difficulties that the students encountered when completing specific tasks.

Card with tasks for each group.

№ 5.

No. 7. The motor boat traveled 112 km upstream of the river and returned to the point of departure, spending 6 hours less on the return journey. Find the speed of the current if the speed of the boat in still water is 11 km/h. Give your answer in km/h.

No. 8. The motor ship travels along the river to its destination 513 km and, after stopping, returns to the point of departure. Find the speed of the ship in still water if the current speed is 4 km/h, the stay lasts 8 hours, and the ship returns to the point of departure 54 hours after departure. Give your answer in km/h.

No. 9. From pier A to pier B, the distance between which is 168 km, the first motor ship set off at a constant speed, and 2 hours after that, the second one set off after it, at a speed 2 km/h higher. Find the speed of the first ship if both ships arrived at point B at the same time. Give your answer in km/h.

Sample thematic control card.

Class ________ Student's full name___________________________________

Job No.

Comment

Cards consultants.

Card No. 1 (consultant)
1. Driving on a straight road
When solving problems involving uniform motion, two situations often occur.

If the initial distance between objects is S, and the velocities of the objects are V1 and V2, then:

a) when objects move towards each other, the time after which they will meet is equal to .

b) when objects move in one direction, the time after which the first object will catch up with the second is equal to , ( V 2 > V 1)

Example 1. The train, having traveled 450 km, was stopped due to snow drift. Half an hour later the path was cleared, and the driver, increasing the speed of the train by 15 km/h, brought it to the station without delay. Find the initial speed of the train if the distance traveled by it to the stop was 75% of the entire distance.
  1. Let's find the entire path: 450: 0.75 = 600 (km)
  2. Let's find the length of the second section: 600 – 450 =150 (km)
  3. Let's create and solve the equation:

X= -75 does not fit the conditions of the problem, where x > 0.

Answer: the initial speed of the train is 60 km/h.

Card No. 2 (consultant)

2. Driving on a closed road

If the length of a closed road is S, and the speeds of objects V 1 and V 2, then:

a) when objects move in different directions, the time between their meetings is calculated by the formula;
b) when objects move in one direction, the time between their meetings is calculated by the formula

Example 2. At a competition on a circuit track, one skier completes a lap 2 minutes faster than the other and an hour later beats him by exactly a lap. How long does it take each skier to complete the circle?

Let S m – length of the ring route and x m/min and y m/min – speeds of the first and second skiers, respectively ( x> y) .

Then S/x min and S/y min – the time it takes the first and second skiers to complete the lap, respectively. From the first condition we obtain the equation. Since the speed of removal of the first skier from the second skier is ( x- y) m/min, then from the second condition we have the equation .

Let's solve the system of equations.

Let's make a replacement S/x= a And S/y= b, then the system of equations will take the form:

. Multiply both sides of the equation by 60 a(a+ 2) > 0.

60(a+ 2) – 60a = a(a+ 2)a 2 + 2a- 120 = 0. Quadratic equation has one positive root a = 10 then b = 12. This means that the first skier completes the circle in 10 minutes, and the second skier in 12 minutes.

Answer: 10 min; 12 min.

Card No. 3 (consultant)

3. Movement along the river

If an object moves with the flow of a river, then its speed is equal to Vflow. =Vob. + Vcurrent

If an object moves against the flow of a river, then its speed is equal to Vagainst the current = V inc. – Vcurrent. The object’s own speed (speed in still water) is equal to

The speed of the river flow is

The speed of the raft is equal to the speed of the river flow.

Example 3. The boat went 50 km downstream of the river, and then traveled 36 km in the opposite direction, which took it 30 minutes longer than along the river. What is the boat's own speed if the speed of the river is 4 km/h?

Let the boat's own speed be X km/h, then its speed along the river is ( x+ 4) km/h, and against the flow of the river ( x- 4) km/h. The time it takes for the boat to move along the river flow is hours, and against the river flow is hours. Since 30 minutes = 1/2 hour, then according to the conditions of the problem we will create the equation =. Multiply both sides of the equation by 2( x+ 4)(x- 4) >0 .

We get 72( x+ 4) -100(x- 4) = (x+ 4)(x- 4) x 2 + 28x- 704 = 0 x 1 =16, x 2 = - 44 (excluded, since x> 0).

So, the boat's own speed is 16 km/h.

Answer: 16 km/h.

IV. Problem solving analysis stage.

Problems that caused difficulty for students are analyzed.

No. 1. From two cities, the distance between which is 480 km, two cars simultaneously drove towards each other. After how many hours will the cars meet if their speeds are 75 km/h and 85 km/h?

  1. 75 + 85 = 160 (km/h) – approach speed.
  2. 480: 160 = 3 (h).

Answer: the cars will meet in 3 hours.

No. 2. From cities A and B, the distance between which is 330 km, two cars simultaneously left towards each other and met after 3 hours at a distance of 180 km from city B. Find the speed of the car that left city A. Give the answer in km/ h.

  1. (330 – 180) : 3 = 50 (km/h)

Answer: the speed of a car leaving city A is 50 km/h.

No. 3. A motorist and a cyclist left at the same time from point A to point B, the distance between which is 50 km. It is known that a motorist travels 65 km more per hour than a cyclist. Determine the speed of the cyclist if it is known that he arrived at point B 4 hours 20 minutes later than the motorist. Give your answer in km/h.

Let's make a table.

Let's create an equation, taking into account that 4 hours 20 minutes =

,

Obviously, x = -75 does not fit the conditions of the problem.

Answer: The cyclist's speed is 10 km/h.

No. 4. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points on a circular track, the length of which is 14 km. How many minutes will it take for the motorcyclists to meet each other for the first time if the speed of one of them is 21 km/h greater than the speed of the other?

Let's make a table.

Let's create an equation.

, where 1/3 hour = 20 minutes.

Answer: in 20 minutes the motorcyclists will pass each other for the first time.

No. 5. From one point on a circular track, the length of which is 12 km, two cars started simultaneously in the same direction. The speed of the first car is 101 km/h, and 20 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h.

Let's make a table.

Let's create an equation.

Answer: the speed of the second car is 65 km/h.

No. 6. A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 36 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

Let's make a table.

Movement before the first meeting

cyclist

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« A bicycle left point A of the circular track» — 251 tasks found

Task B14 ()

(views: 605 , answers: 13 )


A cyclist left point A of the circular track, and 10 minutes later a motorcyclist followed him. 2 minutes after departure, he caught up with the cyclist for the first time, and 3 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 5 km. Give your answer in km/h.

Task B14 ()

(views: 624 , answers: 11 )


A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 10 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 10 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 691 , answers: 11 )


A cyclist left point A of the circular track, and 10 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 15 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 10 km. Give your answer in km/h.

Answer: 60

Task B14 ()

(views: 612 , answers: 11 )


A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 47 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 47 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 608 , answers: 9 )


A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 19 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 19 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 618 , answers: 9 )


A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 2 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 50 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 610 , answers: 9 )


A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 26 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 39 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 ()

(views: 622 , answers: 9 )


A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 20 km. Give your answer in km/h.

The correct answer has not yet been determined

Task B14 (

x 4x, and the speed of their approach is 3 x km/hour

So 3 X

Answer: 80.

Answer: 75

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 46 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 46 km. Give your answer in km/h.

Solution.

prototype.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 75

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 47 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 47 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 36 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 36 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 75

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 21 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 35 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 8 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 8 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer:

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 9 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 12 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 40 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 40 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 0

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 4 minutes after departure, he caught up with the cyclist for the first time, and another 32 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 40 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 80

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 36 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 45 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 80

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 40 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 40 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 1

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 25 minutes after departure, he caught up with the cyclist for the first time, and another 39 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 26 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 65

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 15 minutes after departure, he caught up with the cyclist for the first time, and 42 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 35 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 1

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 54 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 45 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 70

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 24 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 47 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 47 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 70

A cyclist left point A of the circular track, and 10 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 51 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 34 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 9 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 12 minutes after departure, he caught up with the cyclist for the first time, and another 54 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 45 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 18 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer:

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 16 minutes after departure, he caught up with the cyclist for the first time, and another 24 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 20 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 25 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 25 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 150

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 25 minutes after departure, he caught up with the cyclist for the first time, and another 54 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 36 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 28 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 35 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 48 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 36 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 1

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 2 minutes after departure, he caught up with the cyclist for the first time, and another 9 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 25 minutes after departure, he caught up with the cyclist for the first time, and another 57 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 38 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 25 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 20 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 6 minutes after departure, he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 10 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 12 minutes after departure, he caught up with the cyclist for the first time, and 48 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 40 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 10 minutes later a motorcyclist followed him. 1 minute after departure, he caught up with the cyclist for the first time, and another 15 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 25 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 6 minutes after departure, he caught up with the cyclist for the first time, and another 16 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 20 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 12 minutes after departure, he caught up with the cyclist for the first time, and another 18 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 21 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 21 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 10 minutes later a motorcyclist followed him. 2 minutes after departure, he caught up with the cyclist for the first time, and another 28 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 35 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: .

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 27 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 27 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 19 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 19 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 20 minutes after departure, he caught up with the cyclist for the first time, and another 36 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 24 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 4 minutes after departure, he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 20 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

Answer: 110

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 4 minutes after departure, he caught up with the cyclist for the first time, and another 32 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 40 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 48 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 48 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 56 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 42 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 50 minutes later a motorcyclist followed him. 25 minutes after departure, he caught up with the cyclist for the first time, and another 36 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 5 minutes after departure, he caught up with the cyclist for the first time, and another 36 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 48 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 3 minutes after departure, he caught up with the cyclist for the first time, and another 9 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 15 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and another 25 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 25 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.


By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 15 minutes after departure, he caught up with the cyclist for the first time, and another 57 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 38 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.


By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 32 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 40 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.


By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 5 minutes after departure he caught up with the cyclist for the first time, and another 12 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 18 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.


By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 8 minutes after departure, he caught up with the cyclist for the first time, and another 54 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 45 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.


By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 40 minutes later a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 43 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 43 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.


By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

So 3 X= 60 km/h, from which the speed of the cyclist is 20 km/h, and the speed of the motorcyclist is 80 km/h.

Answer: 80.

A cyclist left point A of the circular track, and 20 minutes later a motorcyclist followed him. 4 minutes after departure, he caught up with the cyclist for the first time, and another 21 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 35 km. Give your answer in km/h.

Solution.

This task has not yet been solved, we present the prototype solution.


A cyclist left point A of the circular route. After 30 minutes, he had not yet returned to point A and a motorcyclist followed him from point A. 10 minutes after departure, he caught up with the cyclist for the first time, and another 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the route is 30 km. Give your answer in km/h.

By the time of the first overtaking, the motorcyclist has covered the same distance in 10 minutes as the cyclist did in 40 minutes, therefore, his speed is 4 times greater. Therefore, if the speed of the cyclist is taken to be x km/h, then the speed of the motorcyclist will be equal to 4x, and the speed of their approach is 3 x km/hour

On the other hand, the second time the motorcyclist caught up with the cyclist in 30 minutes, during which time he traveled 30 km more. Consequently, their speed of approach will be 60 km/h.

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