Question

бассейн наполняется водой через первую трубу за 4 часа.Через вторую трубу можно опусташить полный бассейн за 6 часов.За сколько часов наполнится аустой бассейн,если будут работать обе трубы?

Answer 1

Ответ:   12 часов.

Пошаговое объяснение:

бассейн наполняется водой через первую трубу за 4 часа.

Через вторую трубу можно опустошить полный бассейн за 6 часов.

За сколько часов наполнится пустой бассейн,  если будут работать обе трубы?

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Решение.

Производительность 1 трубы равна 1/4 часть бассейна в час

Производительность 2 трубы равна 1/6 часть бассейна в час

Совместная производительность равна

1/4-1/6=> НОК(4;6)=12=>3/12 - 2/12 = 1/12  часть бассейна в час

если будут работать обе трубы пустой бассейн наполнится за

1 : 1/12 = 12 часов

Answer 2

Problem Analysis

We are given that a pool can be filled with water through one pipe in 4 hours and emptied through another pipe in 6 hours. We need to determine how long it will take to fill an empty pool if both pipes are working simultaneously.

Solution

Let's assume that the capacity of the pool is 1 unit (this is an arbitrary assumption and does not affect the calculation).

The first pipe can fill the pool in 4 hours, which means it can fill 1/4 of the pool's capacity in 1 hour. Similarly, the second pipe can empty the pool in 6 hours, which means it can empty 1/6 of the pool's capacity in 1 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.

The net rate of filling the pool per hour can be calculated as follows: Filling rate per hour = Rate of filling by the first pipe - Rate of emptying by the second pipe

Let's calculate the net rate of filling the pool per hour: Filling rate per hour = 1/4 - 1/6

To simplify the calculation, we need to find a common denominator for 4 and 6, which is 12: Filling rate per hour = 3/12 - 2/12 Filling rate per hour = 1/12

This means that when both pipes are working simultaneously, the pool will be filled at a rate of 1/12 of its capacity per hour.

To find the time it takes to fill the empty pool completely, we need to divide the pool's capacity (1 unit) by the net rate of filling per hour (1/12): Time to fill the empty pool = 1 / (1/12) Time to fill the empty pool = 12 hours

Therefore, it will take 12 hours to fill the empty pool if both pipes are working simultaneously.

Answer: The empty pool will be filled in 12 hours if both pipes are working simultaneously.