Question

Из одной точки круговой дорожки стартовали одновременно в одном направлении мистер Фокс пешком и мистер Форд на самокате. Скорость мистера Фокса на 35% больше скорости мистера Форда, и поэтому время от времени Фокс обгоняет Форда. В скольких разных точках дорожки будут происходить обгоны?

Answer 1

Из одной точки круговой дорожки стартовали одновременно в одном направлении мистер Фокс пешком и мистер Форд на самокате. Скорость мистера Фокса на 35% больше скорости мистера Форда, и поэтому время от времени Фокс обгоняет Форда. В скольких разных точках дорожки будут происходить обгоны?

Understanding the problem

We have two individuals, Mr. Fox and Mr. Ford, who start from the same point on a circular track. Mr. Fox is walking, while Mr. Ford is riding a scooter. Mr. Fox's speed is 35% faster than Mr. Ford's speed. We need to determine in how many different points on the track Mr. Fox will overtake Mr. Ford.

Solution

To solve this problem, we need to consider the relative speeds of Mr. Fox and Mr. Ford. Since Mr. Fox's speed is 35% faster than Mr. Ford's speed, we can calculate the ratio of their speeds as follows:

Ratio of speeds = (Speed of Mr. Fox) / (Speed of Mr. Ford) = 1 + 0.35 = 1.35

This means that for every 1 unit of distance covered by Mr. Ford, Mr. Fox will cover 1.35 units of distance.

Since both individuals start from the same point on the circular track, they will meet again when Mr. Fox has covered a distance that is a multiple of the track's circumference. Let's denote the number of times they meet as n.

In each meeting, Mr. Fox will have covered n times the track's circumference, while Mr. Ford will have covered n times the track's circumference multiplied by the ratio of their speeds.

Therefore, we can set up the following equation to find the number of meetings:

n * Circumference = n * Circumference * Ratio of speeds

Simplifying the equation, we get:

n = 1 / (Ratio of speeds - 1)

Now we can substitute the value of the ratio of speeds into the equation and calculate the number of meetings:

n = 1 / (1.35 - 1) = 1 / 0.35 = 2.857

Since the number of meetings must be a whole number, we round down to the nearest integer:

n = 2

Therefore, Mr. Fox and Mr. Ford will meet at two different points on the circular track.

Answer

Mr. Fox and Mr. Ford will overtake each other at two different points on the circular track.