Question

Даю 25 баллов! В бассейн проведено две трубы. С помощью первой трубы бассейн может наполниться за 9 часов, а с помощью второй трубы вся вода из наполненного бассейна может вылиться за 6 часов. Как и на какую часть объема бассейна изменится уровень воды в нем за один час, если одновременно открыть обе трубы?

Answer 1

Первая труба за час повышает уровень воды на 1/9 объёма бассейна.

Вторая труба за час понижает уровень воды на 1/6 объёма бассейна.

Обе вместе: (+1/9 - 1/6) = -1/18

 

Ответ: уровень воды понизится на 1/18 объёма бассейна.

Answer 2

1 - весь бассейн
1/9 часть бассейна наполняется за 1 час через 1-ю трубу
1/6 часть выливается за 1 час через вторую
1/6-1/9=3/18-2/18=1/18 часть
Ответ: за 1 час при двух открытых трубах уровень воды в бассейне понизится на 1/18 часть

Answer 3

Problem Analysis

We are given two pipes that can fill and drain a pool. The first pipe can fill the pool in 9 hours, while the second pipe can drain the entire pool in 6 hours. We need to determine how much the water level in the pool will change in one hour if both pipes are opened simultaneously.

Solution

To solve this problem, we need to calculate the net flow rate of water into or out of the pool when both pipes are open.

Let's assume the volume of the pool is represented by V.

The first pipe can fill the pool in 9 hours, which means it can fill V/9 of the pool's volume in one hour. Similarly, the second pipe can drain the entire pool in 6 hours, which means it can drain V/6 of the pool's volume in one hour.

When both pipes are open, the net flow rate of water into or out of the pool is the difference between the flow rates of the two pipes. Since the second pipe is draining the water, we subtract its flow rate from the flow rate of the first pipe.

Therefore, the net flow rate when both pipes are open is V/9 - V/6 = V(1/9 - 1/6) = V(2/18 - 3/18) = V(-1/18).

Since the flow rate is negative, it means the water level in the pool will decrease. The magnitude of the flow rate, |V(-1/18)|, represents the amount by which the water level will change in one hour.

To find the fraction of the pool's volume by which the water level will change, we divide the magnitude of the flow rate by the volume of the pool: |V(-1/18)| / V = 1/18.

Therefore, the water level in the pool will decrease by 1/18 of its volume in one hour when both pipes are open.

Answer

When both pipes are opened simultaneously, the water level in the pool will decrease by 1/18 of its volume in one hour.

Verification

Let's verify the answer using the given information.

If the pool can be filled in 9 hours using the first pipe, it means that in one hour, 1/9 of the pool's volume is filled. Similarly, if the entire pool can be drained in 6 hours using the second pipe, it means that in one hour, 1/6 of the pool's volume is drained.

When both pipes are open, the net flow rate is 1/9 - 1/6 = -1/18 of the pool's volume per hour. This matches our previous calculation.

Therefore, the answer is verified.

Conclusion

When both pipes are opened simultaneously, the water level in the pool will decrease by 1/18 of its volume in one hour.