Question

В суточном забеге одновременно стартовали Петя и Вася и побежали с постоянными скоростями по круглому стадиону. Вначале Петя бежал быстрее и через час догнал Васю (перегнал на круг). Тогда Вася ускорился на 2 км/ч и через 2 часа сам догнал Петю. После этого тот сразу ускорился ещё на 1 км в час и стал бежать быстрее Васи. Когда Петя теперь догонит Васю?

Answer 1

4 часа понятно? здесь все просто

Answer 2

Problem Analysis

We are given that Peter (Петя) and Vasya (Вася) start a 24-hour race on a circular stadium. Peter initially runs faster and catches up to Vasya after 1 hour. Vasya then accelerates by 2 km/h and catches up to Peter after 2 hours. After that, Peter accelerates by an additional 1 km/h and runs faster than Vasya. We need to determine when Peter will catch up to Vasya.

Solution

Let's break down the problem step by step:

1. Peter catches up to Vasya after 1 hour: - Let's assume Peter's initial speed is x km/h and Vasya's initial speed is y km/h. - Since Peter catches up to Vasya after 1 hour, the distance covered by Peter in 1 hour is equal to the distance covered by Vasya in 1 hour. - Therefore, we can write the equation: x * 1 = y * 1.

2. Vasya catches up to Peter after 2 hours: - After Vasya is caught by Peter, Vasya accelerates by 2 km/h. - Let's assume Vasya's new speed is y + 2 km/h. - Since Vasya catches up to Peter after 2 hours, the distance covered by Vasya in 2 hours is equal to the distance covered by Peter in 2 hours. - Therefore, we can write the equation: (y + 2) * 2 = x * 2.

3. Peter accelerates by an additional 1 km/h: - After Vasya catches up to Peter, Peter accelerates by 1 km/h. - Let's assume Peter's new speed is x + 1 km/h. - We need to find the time it takes for Peter to catch up to Vasya again.

To solve the problem, we can use the equations we derived and solve for the unknown variables.

Solution Steps

1. From the first equation, we have x = y. 2. Substituting x = y into the second equation, we have (y + 2) * 2 = y * 2. 3. Simplifying the equation, we get 2y + 4 = 2y. 4. This equation has no solution, which means there is no valid solution to the problem.

Conclusion

Based on the given information, there is no point at which Peter will catch up to Vasya.