13.133. A swimming pool has three pipes of different cross-sections for draining water using a uniformly pumping pump. The first and second pipes together, with the third pipe closed, empty a full pool in $a$ minutes; the first and third pipes together, with the second pipe closed, empty a full pool in $b$ minutes; and the second and third pipes together, with the first pipe closed, empty a full pool in $c$ minutes. How long does it take to empty a full pool through each pipe individually?
## Solution.

Let the first pipe empty the pool in $x$ min; the second pipe in $y$ min; the third pipe in $z$ min. According to the problem:

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-868.jpg?height=314&width=1016&top_left_y=1311&top_left_x=156)

$$
\begin{aligned}
& z=\frac{2 a b c}{a b+a c-b c} \text { min. } \\
& \text { Answer: in } \frac{2 a b c}{a b+b c-a c}, \frac{2 a b c}{a c+b c-a b} \text { and } \frac{2 a b c}{a b+a c-b c} \text { min. }
\end{aligned}
$$