Question

два велосипедиста участвуют в гонках по круговой дорожке. Первый велосипедист проходит круг за 6 минут, второй за 4 минуты. Через какое время второй велосипедист догонит первого?

Answer 1

Скорость первого - 1/4 круг/мин
Второго - 1/6 круг/мин.
Скорость сближения V =1/4-1/6 = 1/12. Значит второй догонит первого через 12 минут.

Answer 2

Problem Analysis

Two cyclists are participating in a race on a circular track. The first cyclist completes a lap in 6 minutes, while the second cyclist completes a lap in 4 minutes. We need to determine how long it will take for the second cyclist to catch up to the first cyclist.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed of the second cyclist with respect to the first cyclist is the difference in their speeds.

The first cyclist completes a lap in 6 minutes, so his speed is 1 lap per 6 minutes. The second cyclist completes a lap in 4 minutes, so his speed is 1 lap per 4 minutes.

The relative speed of the second cyclist with respect to the first cyclist is the difference in their speeds, which is 1/4 - 1/6 = 1/12 laps per minute.

Now, we can use the formula: Time = Distance / Speed.

Let's assume the distance to be 1 lap (as it is a circular track). The time it takes for the second cyclist to catch up to the first cyclist can be calculated using the relative speed.

Calculation

Using the relative speed formula, we can calculate the time it takes for the second cyclist to catch up to the first cyclist: Time = Distance / Relative Speed Time = 1 / (1/4 - 1/6) Time = 1 / (1/12) Time = 12 minutes

Therefore, the second cyclist will catch up to the first cyclist in 12 minutes.