13.295. A reservoir is supplied by two channels. Water flows out evenly through the first channel, and flows in evenly through the second channel. How many hours will it take for $n$ liters of water to pass through the first channel, if it is known that through the second channel, twice as much water will flow in when it is open for $a$ hours less than the time it takes for $n$ liters to pass through the first channel? If both channels are opened simultaneously, then every hour $a$ liters of water are added to the reservoir.
Solution.

The values of the sought and given quantities are written in the form of a table:

| Channel | Time, h | Volume of water, l | Productivity |
| :---: | :---: | :---: | :---: |
| First | $x$ | $n$ | $\frac{n}{x}$ |
| Second | $x-a$ | $2 n$ | $\frac{2 n}{x-a}$ |

According to the condition $\frac{2 n}{x-a}-\frac{n}{x}=a$,

from which $x=\frac{a^{2}+n+\sqrt{a^{4}+6 a^{2} n+n^{2}}}{2 a}$ (h).

Answer: in $\frac{a^{2}+n+\sqrt{a^{4}+6 a^{2} n+n^{2}}}{2 a}$ h.