Question

Два тела равномерно движутся по окружности. Если они движутся в разные стороны, то встречаются каждые 2 минуты. Если же тела двигаются в одну сторону, то первое тело догоняет второе каждые 10 минут. На сколько секунд быстрее первое тело проходит окружность

Answer 1

Пусть Х - часть окружности, которую первое тело преодолевает за 1 минуту, а Y - часть окружности, которую за одну минуту преодолевает второе тело.

Получаем систему уравнений

X + Y = 1/2                     X = 0,3

X - Y = 1/10 ,  откуда     Y = 0,2

Итак, первое тело за минуту преодолевает 0,3 окружности, а второе тело 0,2 окружности. Следовательно, второе тело проходит окружность за 5 минут, а первое тело за 3 минуты 20 секунд, то есть на 100 секунд быстрее второго. 

Answer 2

Problem Analysis

We are given that two bodies are moving uniformly in a circle. When they move in opposite directions, they meet every 2 minutes. When they move in the same direction, the first body catches up with the second body every 10 minutes. We need to determine how many seconds faster the first body completes the circle.

Solution

Let's assume that the time taken by the first body to complete one circle is T seconds. We need to find the time taken by the second body to complete one circle.

When the bodies move in opposite directions, they meet every 2 minutes. This means that in 2 minutes, the first body completes one circle, and the second body completes T seconds of its circle. Therefore, the time taken by the second body to complete one circle is 2 minutes - T seconds.

When the bodies move in the same direction, the first body catches up with the second body every 10 minutes. This means that in 10 minutes, the first body completes one circle, and the second body completes T seconds of its circle. Therefore, the time taken by the second body to complete one circle is 10 minutes - T seconds.

Since the time taken by the second body to complete one circle is the same in both cases, we can equate the two expressions:

2 minutes - T seconds = 10 minutes - T seconds

Simplifying the equation, we get:

2 minutes = 10 minutes

This equation is not possible, as 2 minutes cannot be equal to 10 minutes. Therefore, there is no solution to this problem.

Answer

There is no solution to the problem. The given scenario is not possible.