Question

Виктор и Кирилл плавают в бассейне по соседним дорожкам. Стартуют они одновременно с противоположных концов бассейна, «встречаются» и плывут дальше. Доплыв до конца дорожки, они мгновенно разворачиваются, опять «встречаются» и так далее. Виктор проплывает дорожку за 6 минут, а Кирилл за 8 минут. Сколько минут пройдёт после старта до момента, когда Виктор впервые догонит Кирилла, плывя с ним в одном направлении?

Answer 1

24 мин
Виктор переплывет дорожку 4 раза, а Кирилл 3, и в конце дорожки Виктор догоняет Кирилла

Answer 2

Problem Analysis

In this problem, Victor and Kirill are swimming in a pool on adjacent lanes. They start at the same time from opposite ends of the pool, meet each other, and continue swimming. After reaching the end of their respective lanes, they instantly turn around and meet again. This process repeats. Victor completes a lane in 6 minutes, while Kirill takes 8 minutes. We need to determine how many minutes it will take for Victor to catch up to Kirill while swimming in the same direction.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed is the difference between the speeds of two objects moving in the same direction. In this case, Victor is swimming faster than Kirill, so his relative speed with respect to Kirill is the difference between their speeds.

Let's calculate the relative speed of Victor with respect to Kirill:

Relative speed = Victor's speed - Kirill's speed

Given that Victor completes a lane in 6 minutes and Kirill completes a lane in 8 minutes, we can calculate their speeds as follows:

Victor's speed = Distance / Time = 1 lane / 6 minutes Kirill's speed = Distance / Time = 1 lane / 8 minutes

Now, let's calculate the relative speed:

Relative speed = Victor's speed - Kirill's speed

To simplify the calculation, we can convert the speeds to a common denominator:

Victor's speed = 1 lane / 6 minutes = 2 lanes / 12 minutes Kirill's speed = 1 lane / 8 minutes = 1.5 lanes / 12 minutes

Relative speed = 2 lanes / 12 minutes - 1.5 lanes / 12 minutes = 0.5 lanes / 12 minutes

This means that Victor catches up to Kirill at a rate of 0.5 lanes every 12 minutes.

To determine how many minutes it will take for Victor to catch up to Kirill, we can set up the following equation:

Distance = Relative speed * Time

Since Victor needs to catch up to Kirill, the distance they need to cover is equal to one lane. Let's solve for time:

1 lane = (0.5 lanes / 12 minutes) * Time

Simplifying the equation:

Time = (1 lane * 12 minutes) / 0.5 lanes

Time = 24 minutes

Therefore, it will take 24 minutes for Victor to catch up to Kirill while swimming in the same direction.

Answer

It will take 24 minutes for Victor to catch up to Kirill while swimming in the same direction.