Question

Если в бассейн вода будет поступать из двух труб одновременно, то он наполнится за 18 мин. А если только из первой, то за 30 мин. За сколько минут наполнится бассейн, если вода будет поступать только из второй трубы?

Answer 1

объем бассейна надо принять за 1.

х - время наполнения бассейна из второй трубы

1/30 + 1/х = 1/18

приводим к общему знаменателю 90х

3х + 90 = 5х

2х=90

х=45 

Answer 2

30 - 18 = 12 минут

12 + 30 = 42 минуты

Ответ 42 минуты

Answer 3

Problem Analysis

We are given the following information: - If water flows into the pool from two pipes simultaneously, the pool fills up in 18 minutes. - If water flows into the pool from only the first pipe, the pool fills up in 30 minutes.

We need to determine how long it will take for the pool to fill up if water flows into the pool only from the second pipe.

Solution

Let's assume that the rate of water flow from the first pipe is x units per minute and the rate of water flow from the second pipe is y units per minute.

From the given information, we can create the following equations:

1. If water flows from both pipes, the pool fills up in 18 minutes: - The rate of water flow from both pipes combined is x + y units per minute. - The total amount of water that flows into the pool in 18 minutes is 18 * (x + y) units.

2. If water flows only from the first pipe, the pool fills up in 30 minutes: - The rate of water flow from the first pipe is x units per minute. - The total amount of water that flows into the pool in 30 minutes is 30 * x units.

Since the pool fills up with the same amount of water in both cases, we can set up the following equation:

18 * (x + y) = 30 * x

Now, let's solve this equation to find the value of y, which represents the rate of water flow from the second pipe.

Calculation

To solve the equation 18 * (x + y) = 30 * x for y, we can simplify it as follows:

18x + 18y = 30x

Rearranging the equation:

18y = 30x - 18x

Simplifying further:

18y = 12x

Dividing both sides by 18:

y = (12/18) * x

Simplifying:

y = (2/3) * x

This equation tells us that the rate of water flow from the second pipe is two-thirds of the rate of water flow from the first pipe.

Answer

If water flows into the pool only from the second pipe, the pool will fill up in the same amount of time it takes for water to flow from the first pipe, multiplied by the ratio of the rates of water flow from the two pipes.

Therefore, if the pool fills up in 30 minutes when water flows from the first pipe, it will take (2/3) * 30 = 20 minutes for the pool to fill up when water flows only from the second pipe.

So, if water flows only from the second pipe, the pool will fill up in 20 minutes.

Conclusion

If water flows into the pool from both pipes simultaneously, the pool fills up in 18 minutes. If water flows into the pool only from the first pipe, the pool fills up in 30 minutes. If water flows into the pool only from the second pipe, the pool will fill up in 20 minutes.