Question

Водой из одной трубы бассейн наполняется за 3 ч, а через вторую трубу полный бассейн опорожняется за 5 ч. За какое время наполнится пустой бассейн, если одновременно будут открыты оба трубы?​

Answer 1

Ответ:

Скорость наполнения бассейна через первый кран: V1 = 1/3 бассейна в час. Скорость опорожнения через второй кран: V2 = 1/5 бассейна в час.

Если открыть оба крана, то их общая скорость наполнения бассейна будет равна сумме скоростей: V = V1 + V2 = 1/3 + 1/5 = 8/15 бассейна в час.

Время наполнения пустого бассейна при открытии обоих кранов вычисляется по формуле: T = 1 / V = 1 / (8/15) = 15/8 часа = 1 час 52,5 минуты.

Ответ: наполнение пустого бассейна займет 1 час 52,5 минуты, если открыть оба крана.

Answer 2

Problem Analysis

We are given that a pool is filled by one pipe in 3 hours and emptied by another pipe in 5 hours. We need to determine how long it will take to fill an empty pool if both pipes are opened simultaneously.

Solution

To solve this problem, we can use the concept of rates. Let's assume that the rate at which the first pipe fills the pool is x (in pool per hour) and the rate at which the second pipe empties the pool is y (in pool per hour).

We are given that the first pipe fills the pool in 3 hours, so the rate of the first pipe can be calculated as 1/3 pool per hour. Similarly, the rate of the second pipe can be calculated as 1/5 pool per hour.

When both pipes are opened simultaneously, the net rate at which the pool is being filled can be calculated by subtracting the rate at which the pool is being emptied from the rate at which it is being filled. Therefore, the net rate can be calculated as (1/3) - (1/5) pool per hour.

To find the time it takes to fill the empty pool, we can divide the pool's capacity by the net rate at which it is being filled. Let's assume the capacity of the pool is C (in pools). Therefore, the time it takes to fill the empty pool can be calculated as C / [(1/3) - (1/5)] hours.

Let's calculate the time it takes to fill the empty pool using the given information.

Calculation

Given: - The first pipe fills the pool in 3 hours. - The second pipe empties the pool in 5 hours.

Let's assume the capacity of the pool is 1 pool (C = 1).

The rate at which the first pipe fills the pool is 1/3 pool per hour. The rate at which the second pipe empties the pool is 1/5 pool per hour.

The net rate at which the pool is being filled when both pipes are opened simultaneously is (1/3) - (1/5) pool per hour.

The time it takes to fill the empty pool can be calculated as 1 / [(1/3) - (1/5)] hours.

Calculation Result

The time it takes to fill the empty pool when both pipes are opened simultaneously is 15/2 hours, which is equivalent to 7.5 hours.

Therefore, it will take 7.5 hours to fill the empty pool when both pipes are opened simultaneously.

Answer

The empty pool will be filled in 7.5 hours if both pipes are opened simultaneously.

Note: The calculation assumes that the rates at which the pipes fill and empty the pool remain constant throughout the process.