Question

В бассейн провено три трубы.По двум трубам вода поступает в бассейн, а по третьей-вытекает. Первая труба наполняет бассейн водой за 6 ч, вторая за 8 ч.По третьей трубе вода из наполненного бассейна вытекает за 4 ч полностью.Какая часть объёма бассейна наполнится водой за час, если вода течёт одновременно по трём трубам?

Answer 1

Если объем бассейна принять за 1,то по первой трубе за час заполняется  1/6 часть бассейна,по второй 1/8 часть и из третьей вытекает 1/4 часть значит за час в бассейне будет


$\frac{1}{6} + \frac{1}{8} - \frac{1}{4} = \frac{4+3-6}{24} = \frac{1}{24}$

Answer 2

Problem Analysis

We have three pipes in a pool: two pipes fill the pool with water, and one pipe drains the water from the pool. 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 the fraction of the pool's volume that will be filled with water in one hour when all three pipes are running simultaneously.

Solution

To solve this problem, we need to calculate the rates at which each pipe fills or drains the pool. Then, we can add the rates of the two filling pipes and subtract the rate of the draining pipe to find the net rate at which the pool is being filled. Finally, we can calculate the fraction of the pool's volume that will be filled in one hour.

Let's calculate the rates of each pipe first:

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

Now, let's calculate the net rate at which the pool is being filled:

- The net filling rate is the sum of the rates of the two filling pipes minus the rate of the draining pipe. - Net filling rate = (filling rate of the first pipe + filling rate of the second pipe) - draining rate of the third pipe. - Net filling rate = (1/6 + 1/8) - 1/4 = 4/24 + 3/24 - 6/24 = 1/24 of the pool's volume per hour.

Therefore, 1/24 of the pool's volume will be filled with water in one hour when all three pipes are running simultaneously.

Answer

When all three pipes are running simultaneously, 1/24 of the pool's volume will be filled with water in one hour.