Question

через первую трубу бассейн наполняется за 1 1/2 часа через вторую вся вода вытекает за 4 часа через третью вся вода вытекает за 3 часа за сколько часов наполнится весь бассейн если включить 3 крана

Answer 1

Ответ бассейн заполнится за 12 часов
производительность труб
первая 1/1,5
вторая 1/4
третья 1/3
вторая и третья труба производительность берем со знаком минус,
т.к.они работают на слив.
1/1,5-1/4-1/3- суммарная производительность
2/3-1/3-1/4=1/3-1/4=4/12-3/12=1/12
время заполнения 1/(1/12)

Answer 2

Problem Analysis

We are given three pipes that fill and drain a pool. The first pipe fills the pool in 1 1/2 hours, the second pipe drains the pool in 4 hours, and the third pipe drains the pool in 3 hours. We need to determine how long it will take to fill the entire pool if all three pipes are turned on.

Solution

To solve this problem, we need to calculate the net rate at which the pool is being filled or drained when all three pipes are turned on.

Let's assume that the capacity of the pool is 1 unit (this could be any unit of measurement, such as liters or gallons).

The first pipe fills the pool in 1 1/2 hours, which means it fills 1/1.5 = 2/3 units per hour. The second pipe drains the pool in 4 hours, which means it drains 1/4 = 1/4 units per hour. The third pipe drains the pool in 3 hours, which means it drains 1/3 = 1/3 units per hour.

When all three pipes are turned on, the net rate at which the pool is being filled or drained is the sum of the rates of the filling pipe and the draining pipes.

Net rate = (filling rate of the first pipe) - (draining rate of the second pipe) - (draining rate of the third pipe)

Net rate = 2/3 - 1/4 - 1/3

To simplify the calculation, we can find a common denominator for the fractions:

Net rate = (8/12) - (3/12) - (4/12)

Net rate = 1/12 units per hour

Since the net rate is positive, it means the pool is being filled.

To find the time it takes to fill the entire pool, we can use the formula:

Time = Capacity / Net rate

Time = 1 / (1/12)

Time = 12 hours

Therefore, it will take 12 hours to fill the entire pool if all three pipes are turned on.

Answer

If all three pipes are turned on, it will take 12 hours to fill the entire pool.