13.293. Two pipes of different cross-sections are connected to a swimming pool. One is a uniform water supply pipe, and the other is a uniform water discharge pipe, with the first pipe filling the pool 2 hours longer than the second pipe empties it. When the pool was filled to $1 / 3$ of its capacity, both pipes were opened, and the pool was found to be empty after 8 hours. How many hours, acting separately, does the first pipe take to fill, and the second pipe to empty the pool?
## Solution.

Let's write down the values of the sought and given quantities in the form of a table:

| Pipe | Time, h | Capacity | Productivity |
| :---: | :---: | :---: | :---: |
| Supply | $x+2$ | 1 | $\frac{1}{x+2}$ |
| Discharge | $x$ | 1 | $\frac{1}{x}$ |
| Both together | 8 | $\frac{1}{3}$ | $\frac{1}{24}$ |

According to the condition $\frac{1}{x}-\frac{1}{x+2}=\frac{1}{24}$, from which $x=6$.

Answer: in 8 and 6 hours.