Question

В бассейн проведено три трубы. По двум трубам вода поступает в бассейн, а по третьей вытекает. Первая труба наполняет бассейн водой за 6 часов, а вторая 8ч. По третьей трубе вода из наполненного бассейна вытекает 4 часа полностью. Какая часть объема бассейна наполниться водой за час, если все три трубы будут течь одновременно?

Answer 1

примем бассейн за 1

1/6 наполняется в час из 1 трубы

1/8  наполняется в час из 2 трубы

1/4 выливается из 3 трубы

1/6+1/8-1/4=(общий знаменатель24)=4/24+3/24-6/24=1/24 бассейна наполниться через 1 час

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 completely in 4 hours. We need to determine what fraction of the pool's volume will be filled with water in one hour if all three pipes are flowing simultaneously.

Solution

To solve this problem, we need to calculate the rate at which water is being added to the pool and the rate at which water is being drained from the pool. Then we can find the net rate of water being added to the pool and calculate the fraction of the pool's volume filled in one hour.

Let's denote the volume of the pool as V. We know that the first pipe fills the pool in 6 hours, so the rate at which water is being added by the first pipe is V/6 per hour. Similarly, the rate at which water is being added by the second pipe is V/8 per hour.

The third pipe drains the pool completely in 4 hours, so the rate at which water is being drained from the pool is V/4 per hour.

To find the net rate of water being added to the pool, we subtract the rate of drainage from the sum of the rates of the two filling pipes:

Net rate = (V/6 + V/8) - V/4

Simplifying this expression, we get:

Net rate = (4V + 3V - 6V) / 24

Net rate = V / 24

Therefore, the net rate of water being added to the pool is V/24 per hour.

To find the fraction of the pool's volume filled in one hour, we divide the net rate by the volume of the pool:

Fraction filled in one hour = (V / 24) / V

Simplifying this expression, we get:

Fraction filled in one hour = 1 / 24

Therefore, one twenty-fourth (1/24) of the pool's volume will be filled with water in one hour if all three pipes are flowing simultaneously.

Answer

If all three pipes are flowing simultaneously, one twenty-fourth (1/24) of the pool's volume will be filled with water in one hour.