Question

К бассейну проведены три трубы. Если по первой и второй трубе вода в бассейн поступает, то через третью трубу вода сливается. Первая труба наполняет бассейн за 6 часов, вторая – за 8 часов. Через третью трубу вода из бассейна вытекает через за 4 часа. За какое время наполнится 3/4 часть бассейна, если включить все три трубы​

Answer 1

Ответ:

18 часов

Пошаговое объяснение:

Обозначим скорость потока из 1й трубы как v1, из 2й - v2, из 3й v3

Тогда:

v1 * 6 = v2 * 8 = v3 * 4 = z

где z - объем бассейна

время, которое потребуется чтобы наполнить бассейн при всех открытых трубах равно (v3 с минусом, потому что вытекает):

t = z / (v1 + v2 - v3)

Выразим v2 через v1:

v2 = (v1 * 6 / 8) = (3/4)v1

Выразим v3 через v1:

v3 = (v1 * 6 / 4) = (6/4)v1

Подставляем:

t = z / (v1 + (3/4)v1 - (6/4)v1)

t = z / (1/4)v1

Заменяем z на v1 * 6

t = (v1 * 6) / (1/4)v1

t = 6 * 4 = 24 часа

а 3/4 части бассейна наполнится соответственно за

24 * 3/4 = 18 часов

Answer 2

Problem Analysis

We have three pipes connected to a pool. The first and second pipes fill the pool with water, while the third pipe drains the water from the pool. We are given that the first pipe fills the pool in 6 hours, the second pipe fills the pool in 8 hours, and the third pipe drains the pool in 4 hours. We need to determine how long it will take to fill 3/4 of the pool if all three pipes are turned on.

Solution

To solve this problem, we can calculate the rates at which each pipe fills or drains the pool. Then, we can determine the net rate at which the pool is being filled or drained when all three pipes are turned on. Finally, we can use this net rate to calculate the time it takes to fill 3/4 of the pool.

Let's start by calculating the rates at which each pipe fills or drains the pool.

- The first pipe fills the pool in 6 hours, so its filling rate is 1/6 of the pool per hour. - The second pipe fills the pool in 8 hours, so its filling rate is 1/8 of the pool per hour. - The third pipe drains the pool in 4 hours, so its draining rate is 1/4 of the pool per hour.

Now, let's calculate the net rate at which the pool is being filled or drained when all three pipes are turned on. Since the third pipe drains the pool, we subtract its draining rate from the sum of the filling rates of the first and second pipes.

- Net filling rate = (1/6 + 1/8) - 1/4 = 1/24 of the pool per hour.

Now that we have the net filling rate, we can calculate the time it takes to fill 3/4 of the pool. We can use the formula:

- Time = Amount / Rate

In this case, the amount is 3/4 of the pool, and the rate is 1/24 of the pool per hour.

- Time = (3/4) / (1/24) = (3/4) * (24/1) = 18 hours.

Therefore, it will take 18 hours to fill 3/4 of the pool if all three pipes are turned on.

Answer

If all three pipes are turned on, it will take 18 hours to fill 3/4 of the pool.

[[1]]