Question

Том и Джерри бегают друг за другом по трассе в виде восьмёрки (см. рисунок). Они бегут в одном направлении и с постоянными скоростями. В начальный момент Джерри был точно над Томом. Через 20 минут Том оказался точно над Джерри, причём ни один из них не успел пробежать трассу полностью. В момент, когда Джерри пробежал ровно один круг с начала пути, Том наконец догнал его. Сколько времени Том гнался за Джерри?

Answer 1

40 мин может быт.и он 2 круг догналься

Answer 2

Problem Analysis

Tom and Jerry are running in a figure-eight-shaped track in the same direction with constant speeds. At the initial moment, Jerry is directly above Tom. After 20 minutes, Tom is directly above Jerry, and neither of them has completed the full track. We need to determine how much time Tom chased Jerry.

Solution

Let's assume that the time it takes for Tom to complete one lap is T minutes. Since Jerry completes one lap in the same time, we can say that Jerry's speed is equal to the track length divided by T.

After 20 minutes, Tom is directly above Jerry. This means that Tom has covered 20 minutes worth of distance, while Jerry has covered 20 minutes worth of distance minus one lap. Therefore, the distance covered by Tom is equal to the distance covered by Jerry plus the track length.

Using the formula distance = speed × time, we can write the following equation:

Tom's distance = Jerry's distance + track length

Let's denote the track length as L and Jerry's speed as S. The distance covered by Tom after 20 minutes is 20S (since Tom's speed is also S), and the distance covered by Jerry is 20S - L.

Therefore, we have the equation:

20S = (20S - L) + L

Simplifying the equation, we get:

20S = 20S

This equation is true for any value of S. It means that Tom and Jerry will always meet after 20 minutes.

Since Tom and Jerry meet after 20 minutes, and Tom takes T minutes to complete one lap, we can conclude that Tom chased Jerry for 20 - T minutes.

Answer

Tom chased Jerry for 20 - T minutes, where T is the time it takes for Tom to complete one lap.

Please note that the time it takes for Tom to complete one lap (T) is not provided in the question, so we cannot determine the exact amount of time Tom chased Jerry without that information.