Question

Вода, поступающая в первую трубу, может наполнить бассейн за 6ч, а вода, вытекающая из второй трубы, может его опорожнить за 15ч. За сколько часов наполниться бассейн, если обе трубы будут работать одновременно?

Answer 1

1=t*(1/6-1/15)
t=1/(1/6-1/15)=6*15/(15-6)=6*15/9 = 10 часов

Answer 2

За один час бассейн заполняется на 1/6 часть.
Опорожняется бассейн за 1 час на 1/15
То есть за 1 час бассейн наполнится на
 1/6 - 1/15 = 5/30 - 2/30 = 3/30 = 1/10 (части)
Чтобы заполнился весь бассейн нужно 10 раз по 1/10, то есть 10 часов

Answer 3

Problem Analysis

We are given that the first pipe can fill the pool in 6 hours, and the second pipe can empty the pool in 15 hours. We need to determine how long it will take to fill the pool if both pipes are working simultaneously.

Solution

To solve this problem, we can consider the rates at which the pipes fill and empty the pool. Let's assume that the pool has a capacity of 1 unit (for simplicity).

The first pipe can fill the pool in 6 hours, which means it fills at a rate of 1/6 units per hour. Similarly, the second pipe can empty the pool in 15 hours, which means it empties at a rate of 1/15 units per hour.

When both pipes are working simultaneously, the net rate of filling the pool will be the difference between the filling rate of the first pipe and the emptying rate of the second pipe.

Net filling rate = Filling rate of first pipe - Emptying rate of second pipe = 1/6 - 1/15 = (5/30) - (2/30) = 3/30 = 1/10 units per hour

Since the net filling rate is 1/10 units per hour, it will take 10 hours to fill the pool completely.

Answer

If both pipes are working simultaneously, it will take 10 hours to fill the pool completely.

Source:

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