Question

226*. Папа и сын плыли в лодке против течения реки. Сын уронил за борт папину шляпу .Через 20 минут папа заметил пропажу, развернул лодку и стал догонять шляпу. При этом лодка плыла с той же собственной скоростью. Через сколько минут они догонят шляпу?1)С какой скоростью удалялись лодка и шляпа?.........................................................................2)С какой скоростью сближались лодка и шляпа?..........................................................................Лодка и шляпа удалялись и сближались на одно и тоже расстояние с ...... скоростью, поэтому папа с сыном догонят шляпу через ........... минут.

Answer 1

Движение лодки от шапки 20км/ч и движение лодки до шапки тоже 20км/ч 

Answer 2

Problem Analysis

In this problem, a father and son are in a boat that is moving against the current of a river. The son accidentally drops the father's hat overboard. After 20 minutes, the father notices the missing hat, turns the boat around, and starts chasing after the hat. The boat and the hat are moving at the same speed. We need to determine how long it will take for the father and son to catch up to the hat.

Solution

To solve this problem, we need to consider the following:

1) The speed at which the boat and the hat are moving away from each other. 2) The speed at which the boat and the hat are moving towards each other.

Let's analyze these two aspects in detail.

Speed at Which the Boat and the Hat are Moving Away from Each Other

When the boat and the hat are moving away from each other, we can assume that the combined speed of the boat and the current is equal to the speed of the hat. Let's denote the speed of the boat as B and the speed of the current as C. Therefore, the speed of the hat can be represented as B + C.

Speed at Which the Boat and the Hat are Moving Towards Each Other

When the boat turns around and starts chasing the hat, it is moving towards the hat with a speed equal to the speed of the hat. Therefore, the speed at which the boat and the hat are moving towards each other is also B + C.

Since the boat and the hat are moving away from each other and towards each other at the same speed, the time it takes for the boat to catch up to the hat will be the same as the time it took for the hat to move away from the boat.

Therefore, the boat and the son will catch up to the hat in 20 minutes.

Summary

In summary, the boat and the hat are moving away from each other and towards each other at the same speed. Therefore, the boat and the son will catch up to the hat in 20 minutes.