Question

Бассейн наполняется двумя трубами за 3 часа .Первая труба ,действуя одна ,может заполнить бассейн на 8 часов медленнее,чем вторая труба.Зсколько часов наполнит бассейн одна первая труба?

Answer 1

Вот так вот илик мало баллов
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Answer 2

Problem Analysis

We are given that a pool is being filled by two pipes, and it takes 3 hours to fill the pool when both pipes are working together. We are also given that the first pipe, when working alone, fills the pool 8 hours slower than the second pipe. We need to determine how many hours it would take for the first pipe to fill the pool on its own.

Solution

Let's assume that the second pipe can fill the pool in x hours. According to the given information, the first pipe takes 8 hours longer than the second pipe to fill the pool on its own. Therefore, the first pipe would take (x + 8) hours to fill the pool on its own.

We know that when both pipes are working together, they can fill the pool in 3 hours. This means that in 1 hour, they can fill 1/3 of the pool.

Now, let's calculate the rate at which each pipe fills the pool. The second pipe can fill the pool in x hours, so its rate is 1/x of the pool per hour. Similarly, the first pipe can fill the pool in (x + 8) hours, so its rate is 1/(x + 8) of the pool per hour.

When both pipes are working together, their combined rate is 1/3 of the pool per hour. Therefore, we can write the equation:

1/x + 1/(x + 8) = 1/3

To solve this equation, we can multiply both sides by 3x(x + 8) to eliminate the denominators:

3(x + 8) + 3x = x(x + 8)

Simplifying the equation:

3x + 24 + 3x = x^2 + 8x

6x + 24 = x^2 + 8x

Rearranging the equation:

x^2 + 2x - 24 = 0

Now, we can solve this quadratic equation to find the value of x, which represents the number of hours it takes for the second pipe to fill the pool on its own.