How to solve traffic problems. A cyclist left point A of the circular track (cm)

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

(impressions: 606 , 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 a second time. Find the speed of the biker if the track is 5 km long. Give your answer in km / h.

(impressions: 625 , 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 10 minutes after that he caught up with him a second time. Find the speed of the biker if the track is 10 km long. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 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 15 minutes later he caught up with him a second time. Find the speed of the motorcyclist if the track is 10 km long. Give your answer in km / h.

Answer: 60

(impressions: 613 , answers: 11 )

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

The correct answer has not yet been determined

(impressions: 610 , 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 19 minutes later he caught up with him a second time. Find the speed of the motorcyclist if the track is 19 km long. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 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 30 minutes after that he caught up with him a second time. Find the speed of the biker if the track is 50 km. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 613 , 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 26 minutes later he caught up with him a second time. Find the speed of the biker if the track is 39 km. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 622 , answers: 9 )

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

The correct answer has not yet been determined

From point A of the circular track, the length of which is 75 km, two cars simultaneously started in the same direction. The speed of the first car is 89 km / h, the speed of the second car is 59 km / h. How many minutes after the start will the first car be ahead of the second by exactly one lap?

The solution of the problem

This lesson shows how, using a physical formula to determine the time when uniform movement:, make up the proportion to determine the time when one car will overtake another in a circle. When solving the problem, a clear sequence of actions is indicated for solving such problems: we enter a specific designation for what we want to find, write down the time it takes one and the second car to overcome a certain number of laps, given that this time is the same value- we equate the obtained equalities. The solution is to find an unknown quantity in a linear equation. To get the results, be sure to remember to substitute the number of circles obtained in the formula for determining the time.

The solution to this problem is recommended for 7th grade students when studying the topic “Mathematical language. Mathematical model" ( Linear Equation with one variable "). In preparation for the OGE, the lesson is recommended when repeating the topic “Mathematical language. Mathematical model".

More than 80,000 real-life USE problems in 2020

You are not logged in to the "" system. This does not interfere with viewing and solving tasks. Open bank of USE problems in mathematics, but to participate in the competition of users to solve these problems.

Search result for USE tasks in mathematics on request:
« a cyclist left point a of the circular track and 30 minutes later followed him»- found 106 tasks

(impressions: 613 , answers: 11 )

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

(impressions: 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 30 minutes after that he caught up with him a second time. Find the speed of the biker if the track is 50 km. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 613 , 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 26 minutes later he caught up with him a second time. Find the speed of the biker if the track is 39 km. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 628 , answers: 9 )

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 40 minutes after that he caught up with him a second time. Find the speed of the biker if the track is 40 km. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 611 , answers: 8 )

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 39 minutes after that he caught up with him a second time. Find the speed of the biker if the track is 39 km long. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 628 , answers: 8 )

A cyclist left point A of the circular track, and 30 minutes later a motorcyclist followed him. 15 minutes after the departure, he caught up with the cyclist for the first time, and another 54 minutes after that he caught up with him a second time. Find the speed of the biker if the track is 45 km. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 639 , answers: 8 )

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 44 minutes after that he caught up with him a second time. Find the speed of the biker if the track is 33 km. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 899 , answers: 7 )

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 30 minutes after that he caught up with him a second time. Find the speed of the motorcyclist if the track is 30 km long. Give your answer in km / h.

The correct answer has not yet been determined

(impressions: 591 , answers: 7 )

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 49 minutes later he caught up with him a second time. Find the speed of the biker if the track is 49 km. Give your answer in km / h.

The same formulas are true: \ [(\ large (S = v \ cdot t \ quad \ quad \ quad v = \ dfrac St \ quad \ quad \ quad t = \ dfrac Sv)) \]
from one point in one direction with speeds \ (v_1> v_2 \).

Then if \ (l \) is the length of the circle, \ (t_1 \) is the time after which they will be at the same point for the first time, then:

That is, for \ (t_1 \) the first body will cover the distance \ (l \) greater than the second body.

If \ (t_n \) is the time after which they are in the \ (n \) th time at one point, then the following formula is valid: \ [(\ large (t_n = n \ cdot t_1)) \]

\ (\ blacktriangleright \) Let the two bodies begin to move from different points in the same direction with speeds \ (v_1> v_2 \).

Then the problem is easily reduced to the previous case: you need to find first the time \ (t_1 \), after which they will be at the same point for the first time.
If at the moment of the start of movement the distance between them \ (\ buildrel \ smile \ over (A_1A_2) = s \), then:

Task 1 # 2677

Task level: Easier than the exam

Two athletes start in the same direction from diametrically opposite points of the circular track. They run at different, inconsistent speeds. It is known that the moment the athletes first caught up, they stopped training. How many more laps did the athlete run at a faster average speed than the other athlete?

Let's call the athlete with the highest average speed first. First, the first athlete had to run half a lap to reach the start of the second athlete. After that, he had to run as much as the second athlete ran (roughly speaking, after the first athlete ran half a circle, before the meeting he had to run every meter of the track that the second athlete ran, and as many times as the second athlete ran this meter. ).

Thus, the first athlete ran \ (0.5 \) more laps.

Answer: 0.5

Quest 2 # 2115

Task level: Easier than the exam

Murzik the cat runs in a circle from the dog Sharik. The speeds of Murzik and Sharik are constant. It is known that Murzik runs \ (1.5 \) times faster than Sharik and in \ (10 ​​\) minutes they run two laps in total. How many minutes will the Ball run one lap?

Since Murzik runs \ (1.5 \) times faster than Sharik, then in \ (10 ​​\) minutes Murzik and Sharik in total run the same distance that Sharik would run in \ (10 ​​\ cdot (1 + 1.5 ) = 25 \) minutes. Therefore, the Ball runs two circles in \ (25 \) minutes, then one circle the Ball runs in \ (12.5 \) minutes

Answer: 12.5

Quest 3 # 823

Task level: Equal to the exam

From point A of the circular orbit of the distant planet, two meteorites flew out simultaneously in the same direction. The speed of the first meteorite is 10,000 km / h more than the speed of the second. It is known that they met for the first time after departure 8 hours later. Find the length of the orbit in kilometers.

The moment they first met, the difference in the distances they flew is equal to the length of the orbit.

In 8 hours the difference became \ (8 \ cdot 10,000 = 80,000 \) km.

Answer: 80000

Quest 4 # 821

Task level: Equal to the exam

The thief who stole the purse runs away from the owner of the purse along a circular road. The speed of the thief is 0.5 km / h more than the speed of the owner of the purse who runs after him. In how many hours will the thief catch up with the owner of the purse for the second time, if the length of the road along which they run is 300 meters (consider that the first time he caught up with her after the theft of the purse)?

First way:

The thief will catch up with the owner of the purse for the second time at the moment when the distance that he will run becomes 600 meters more than the distance that the owner of the purse will run (from the moment of the theft).

Since his speed is \ (0.5 \) km / h more, then in an hour he runs 500 meters more, then in \ (1: 5 = 0.2 \) hours he runs \ (500: 5 = 100 \) meters more. He will run 600 meters more in \ (1 + 0.2 = 1.2 \) hours.

Second way:

Let \ (v \) km / h be the speed of the lady of the handbag, then
\ (v + 0.5 \) km / h - thief's speed.
Let \ (t \) h be the time after which the thief will catch up with the mistress of the handbag a second time, then
\ (v \ cdot t \) - the distance that the mistress of the handbag will run in \ (t \) h,
\ ((v + 0.5) \ cdot t \) - the distance that the thief will run in \ (t \) hours.
The thief will catch up with the owner of the purse for the second time at the moment when he runs exactly 2 laps more than her (that is, \ (600 \) m = \ (0.6 \) km), then \ [(v + 0.5) \ cdot t - v \ cdot t = 0.6 \ qquad \ Leftrightarrow \ qquad 0.5 \ cdot t = 0.6, \] whence \ (t = 1,2 \) h.

Answer: 1.2

Task 5 # 822

Task level: Equal to the exam

Two motorcyclists start at the same time from the same point of the circular track in different directions. The first rider's speed is twice that of the second. An hour after the start, they met for the third time (consider that the first time they met after the start). Find the speed of the first rider if the track is 40 km. Give your answer in km / h.

At that moment, when the motorcyclists met for the third time, the total distance they covered was \ (3 \ cdot 40 = 120 \) km.

Since the speed of the first is 2 times higher than the speed of the second, it covered part of 120 km 2 times more than the second, that is, 80 km.

Since they met for the third time in an hour, the first traveled 80 km in an hour. Its speed is 80 km / h.

Answer: 80

Task 6 # 824

Task level: Equal to the exam

Two runners start simultaneously in one direction from two diametrically opposite points of a circular track, the length of which is 400 meters. In how many minutes will the runners level up for the first time if the first runner runs 1 kilometer more in an hour than the second?

In an hour, the first runner runs 1000 meters more than the second, which means he will run 100 meters more in \ (60: 10 = 6 \) minutes.

The initial distance between the runners is 200 meters. They will level up when the first runner runs 200 meters more than the second.

This will happen in \ (2 \ cdot 6 = 12 \) minutes.

Answer: 12

Task 7 # 825

Task level: Equal to the exam

A tourist left town M along a circular road 220 kilometers long, and 55 minutes later a motorist followed him from town M. 5 minutes after departure, he caught up with the tourist for the first time, and 4 hours after that he caught up with him a second time. Find the speed of the tourist. Give your answer in km / h.

First way:

After the first meeting, the motorist caught up with the tourist (for the second time) after 4 hours. By the time of the second meeting, the motorist had driven more laps than the tourist had traveled (that is, by \ (220 \) km).

Since during these 4 hours the motorist overtook the tourist by \ (220 \) km, the speed of the motorist is \ (220: 4 = 55 \) km / h more than the speed of the tourist.

Let now the speed of the tourist \ (v \) km / h, then before the first meeting he managed to pass \ the motorist managed to pass \ [(v + 55) \ dfrac (5) (60) = \ dfrac (v + 55) (12) \ \ text (km). \] Then \ [\ dfrac (v + 55) (12) = v, \] whence we find \ (v = 5 \) km / h.

Second way:

Let \ (v \) km / h be the speed of the tourist.
Let \ (w \) km / h be the speed of the motorist. Since \ (55 \) minutes \ (+ 5 \) minutes \ (= 1 \) hour, then
\ (v \ cdot 1 \) km - the distance traveled by the tourist before the first meeting. Since \ (5 \) minutes \ (= \ dfrac (1) (12) \) hours, then
\ (w \ cdot \ dfrac (1) (12) \) km - the distance traveled by the motorist before the first meeting. The distances they traveled before the first meeting are equal: \ Over the next 4 hours, the motorist drove more than the tourist passed the circle (on \(220\) \ \

When using in the exercise values ​​that are related to distance (speed, length of a circle), they can be solved by converting them to displacement in a straight line.

The greatest difficulty for schoolchildren in Moscow and other cities, as practice shows, is caused by the problems of circular movement in the exam, the search for an answer in which is associated with the use of an angle. To solve the exercise, you can specify the circumference as part of the circle.

You can repeat these and other algebraic formulas in the "Theoretical Reference" section. In order to learn how to apply them in practice, go through the exercises on this topic in the "Catalog".