Question

ВНИМАНИЕ СРОЧНО через первую трубу бассейн наполняется за 2 часа , а через вторую - опорожняется за 3 часа . За какое время наполнится пустой бассейн , если одновременно открыть две трубы.

Answer 1

Скорость наполнения бассейна через первую трубу 1/2 бассейна в час
скорость опорожнения бассейна  1/3 бассейна в час.
скорость наполнения бассейна при открытии двух труб будет
1/2 - 1/3 = 3/6- 2/6 = 1/6 бассейна наполнится за 1 час.
1 : 1/6 = 6 
Ответ: за 6 часа

Answer 2

Problem Analysis

We have two pipes: one fills the pool in 2 hours, and the other empties the pool in 3 hours. We need to find out how long it will take to fill an empty pool if both pipes are opened simultaneously.

Solution

To solve this problem, we can calculate the rates at which each pipe fills or empties the pool. Then we can determine the net rate at which the pool is being filled or emptied when both pipes are open. Finally, we can use this net rate to calculate the time it takes to fill the empty pool.

Let's denote the rate at which the first pipe fills the pool as R1 (in pool per hour) and the rate at which the second pipe empties the pool as R2 (in pool per hour).

Given that the first pipe fills the pool in 2 hours, we can calculate R1 as the reciprocal of the time taken to fill the pool: R1 = 1/2.

Similarly, given that the second pipe empties the pool in 3 hours, we can calculate R2 as the reciprocal of the time taken to empty the pool: R2 = 1/3.

Now, when both pipes are open, the net rate at which the pool is being filled or emptied is the difference between the rates of the two pipes: Net rate = R1 - R2.

To find the time it takes to fill the empty pool, we can use the formula: Time = 1 / Net rate.

Let's calculate the net rate and the time it takes to fill the empty pool.

Calculation

The rate at which the first pipe fills the pool: R1 = 1/2.

The rate at which the second pipe empties the pool: R2 = 1/3.

The net rate when both pipes are open: Net rate = R1 - R2 = (1/2) - (1/3) = 1/6.

The time it takes to fill the empty pool: Time = 1 / Net rate = 1 / (1/6) = 6 hours.

Answer

If both pipes are opened simultaneously, it will take 6 hours to fill the empty pool.