13.292. Two "mechanical moles" of different power, working simultaneously from different ends of the tunnel, could dig it in 5 days. In reality, however, both "moles" were used sequentially from one side of the tunnel, with the first digging $1 / 3$, and the second - the remaining $2 / 3$ of its length. The entire job took 10 days in this case. How many days would each "mole," working alone, need to dig the tunnel?
## Solution.

Let the length of the tunnel be 1. Let $x, y$ be the powers of the first and second "moles" respectively.

According to the problem, we have the system $\left\{\begin{array}{l}5(x+y)=1, \\ \frac{1}{3 x}+\frac{2}{3 y}=10\end{array}\right.$, from which $x=\frac{1}{15}, y=\frac{2}{15}$.

Then the first "mole" will dig the tunnel alone in $3 \times \frac{1}{x}=15$ (days), and the second $-3 \times \frac{1}{y}=7.5$ (days).

Answer: 15 and 7.5 days.