Question

вася и петя , поссорившись , разбежались с одинаковыми скоростями в противоположных направлениях . Через 5 мин. Вася спохватился , повернул назад и, увеличив скорость . побежал догонять петю . Во сколько раз увеличил скорость Вася, если он догнал Петю через 5 мин. после того , как повернул назад?

Answer 1

вася догнал петю увеличив скорость в 3 раза

 

Answer 2

Problem Analysis

Vasya and Petya had an argument and ran away from each other at the same speed. After 5 minutes, Vasya realized his mistake, turned back, and increased his speed to catch up with Petya. We need to determine how much Vasya increased his speed if he caught up with Petya 5 minutes after turning back.

Solution

Let's assume the initial speed of Vasya and Petya is x units per minute. Since they ran in opposite directions, their relative speed is 2x units per minute.

After 5 minutes, Vasya turned back and increased his speed. Let's assume his new speed is y units per minute. Now, the relative speed between Vasya and Petya is (y + x) units per minute.

Since Vasya caught up with Petya 5 minutes after turning back, the distance covered by Vasya in those 5 minutes is equal to the distance covered by Petya in the entire time.

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

5(y + x) = d

Where d is the total distance covered by Petya.

Now, let's solve the equation to find the value of y.

5(y + x) = d

Simplifying the equation:

5y + 5x = d

Since Vasya caught up with Petya, the distance covered by Vasya is equal to the distance covered by Petya. Therefore, we can replace d with 5x:

5y + 5x = 5x

Subtracting 5x from both sides:

5y = 0

Dividing both sides by 5:

y = 0

This means that Vasya did not increase his speed at all. He caught up with Petya by running at the same speed.

Answer

Vasya did not increase his speed. He caught up with Petya by running at the same speed.