Posted on 03/23/2018
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 30 minutes later I 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
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Svetl-ana02-02
23 hours ago
If I understood the condition correctly, the motorcyclist left half an hour after the cyclist started. In this case the solution looks like this.
A cyclist covers the same distance in 40 minutes, and a motorcyclist in 10 minutes; therefore, the speed of a motorcyclist is four times the speed of a cyclist.
Let's say a cyclist moves at a speed of x km/h, then the speed of the motorcyclist is 4x km/h. Before the second meeting, (1/2 + 1/2 + 1/6) = 7/6 hours will pass from the moment the cyclist starts and (1/2 + 1/6) = 4/6 hours from the moment the motorcyclist starts. By the time of the second meeting, the cyclist will have covered (7x/6) km, and the motorcyclist will have covered (16x/6) km, having overtaken the cyclist by one lap, i.e. having traveled 30 km more. We get the equation.
16x/6 - 7x/6 = 30, from where
So, the cyclist was traveling at a speed of 20 km/h, which means the motorcyclist was traveling at a speed of (4*20) = 80 km/h.
Answer. The speed of the motorcyclist is 80 km/h.
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Vdtes-t
22 hours ago
If the solution is in km/h, then the time must be expressed in hours.
Let's denote
v speed of the cyclist
m motorcyclist speed
After ½ hour, a motorcyclist followed the cyclist from point A. ⅙ hour after departure he caught up with the cyclist for the first time
We write down the path traveled before the first meeting in the form of an equation:
and another ½ hour after that, the motorcyclist caught up with him for the second time.
We write down the path traveled to the second meeting in the form of an equation:
We solve a system of two equations:
We simplify the first equation (multiplying both sides by 6):
Substitute m into the second equation:
The cyclist's speed is 20 km/h
Determining the speed of a motorcyclist
Answer: the speed of the motorcyclist is 80 km/h
From point A of a circular track, the length of which is 75 km, two cars started simultaneously 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?
Problem solution
This lesson shows how, using physical formula to determine the time during uniform motion: draw up a proportion to determine the time when one car overtakes another in a circle. When solving the problem, a clear sequence of actions is indicated for solving similar problems: we enter a specific designation for what we want to find, write down the time it takes one and the second car to cover a certain number of laps, taking into account that this time is same size– we equate the resulting equalities. The solution involves finding the unknown quantity in a linear equation. To get the results, you must remember to substitute the number of laps obtained into 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"). When preparing for the OGE, the lesson is recommended when repeating the topic “Mathematical language. Mathematical model".
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