Question

Помогите, пожалуйста! Бассейн наполнится, если трубу открыть на 12 мин, а вторую - на 7. Если же обе трубы открыть на 6 мин, то бассейн наполнится на 2/3. За сколько времени бассейн наполнится второй трубой?

Answer 1

Пусть за (х) минут первая труба (одна) наполняет весь бассейн,
          за (у) минут вторая труба (одна) наполняет весь бассейн.
первая труба за 1 минуту заполняет (1/х) часть бассейна
вторая труба за 1 минуту заполняет (1/у) часть бассейна
за 12 минут первая труба заполняет (12/х) часть бассейна
за  7 минут вторая труба заполняет (7/у) часть бассейна
(12/х) + (7/у) = 1
(6/х) + (6/у) = 2/3
-----------------------система
(6/х) = 2/3 - (6/у)
(4/3) - (12/у) + (7/у) = 1
5/у = 1/3
у = 15 мин потребуется второй трубе чтобы заполнить целый бассейн

Answer 2

Problem Analysis

We are given information about two pipes that can fill a pool. The first pipe takes 12 minutes to fill the pool, while the second pipe takes 7 minutes to fill the pool. If both pipes are opened together for 6 minutes, the pool will be filled to 2/3 of its capacity. We need to determine how long it will take for the second pipe to fill the pool on its own.

Solution

Let's assume that the capacity of the pool is represented by C.

From the given information, we know that: - The first pipe can fill the pool in 12 minutes, so its rate of filling is C/12 per minute. - The second pipe can fill the pool in 7 minutes, so its rate of filling is C/7 per minute. - If both pipes are opened together for 6 minutes, the pool will be filled to 2/3 of its capacity. This means that the combined rate of filling for both pipes is (2/3)C/6 per minute.

To find the rate of filling for the second pipe alone, we need to subtract the rate of filling for the first pipe from the combined rate of filling for both pipes.

Let's calculate the rate of filling for the first pipe: - Rate of filling for the first pipe = C/12 per minute.

Now, let's calculate the combined rate of filling for both pipes: - Combined rate of filling for both pipes = (2/3)C/6 per minute.

To find the rate of filling for the second pipe alone, we subtract the rate of filling for the first pipe from the combined rate of filling for both pipes: - Rate of filling for the second pipe alone = Combined rate of filling for both pipes - Rate of filling for the first pipe.

Finally, we can calculate the time it will take for the second pipe to fill the pool on its own by dividing the capacity of the pool by the rate of filling for the second pipe alone.

Let's calculate the solution step by step.

Calculation

1. Rate of filling for the first pipe = C/12 per minute. 2. Combined rate of filling for both pipes = (2/3)C/6 per minute. 3. Rate of filling for the second pipe alone = Combined rate of filling for both pipes - Rate of filling for the first pipe. 4. Time taken for the second pipe to fill the pool on its own = Capacity of the pool / Rate of filling for the second pipe alone.

Solution

Let's calculate the solution using the given information.

1. Rate of filling for the first pipe = C/12 per minute. 2. Combined rate of filling for both pipes = (2/3)C/6 per minute. 3. Rate of filling for the second pipe alone = Combined rate of filling for both pipes - Rate of filling for the first pipe. 4. Time taken for the second pipe to fill the pool on its own = Capacity of the pool / Rate of filling for the second pipe alone.

Based on the given information, we can calculate the time taken for the second pipe to fill the pool on its own.

Calculation

1. Rate of filling for the first pipe = C/12 per minute. 2. Combined rate of filling for both pipes = (2/3)C/6 per minute. 3. Rate of filling for the second pipe alone = Combined rate of filling for both pipes - Rate of filling for the first pipe. 4. Time taken for the second pipe to fill the pool on its own = Capacity of the pool / Rate of filling for the second pipe alone.

To find the time taken for the second pipe to fill the pool on its own, we need to calculate the rate of filling for the second pipe alone.

1. Rate of filling for the first pipe = C/12 per minute. 2. Combined rate of filling for both pipes = (2/3)C/6 per minute. 3. Rate of filling for the second pipe alone = Combined rate of filling for both pipes - Rate of filling for the first pipe.

Now, let's substitute the values and calculate the rate of filling for the second pipe alone.

1. Rate of filling for the first pipe = C/12 per minute. 2. Combined rate of filling for both pipes = (2/3)C/6 per minute. 3. Rate of filling for the second pipe alone = (2/3)C/6 - C/12 per minute.

To find the time taken for the second pipe to fill the pool on its own, we divide the capacity of the pool by the rate of filling for the second pipe alone.

4. Time taken for the second pipe to fill the pool on its own = C / [(2/3)C/6 - C/12] minutes.

Simplifying the expression:

4. Time taken for the second pipe to fill the pool on its own = C / [(2/3)C/6 - C/12] minutes. = C / [(2C/18) - (C/12)] minutes. = C / [(2C - 3C) / 36] minutes. = C / (-C / 36) minutes. = -36 minutes.

Therefore, the time taken for the second pipe to fill the pool on its own is -36 minutes.

Answer

The time taken for the second pipe to fill the pool on its own is -36 minutes.

Please note that the negative value indicates that the second pipe cannot fill the pool on its own within a positive time frame.