13.228. Two workers were assigned to manufacture a batch of identical parts. After the first worked for 2 hours and the second for 5 hours, it turned out that they had completed half of the entire work. Working together for another 3 hours, they found that they had 0.05 of the entire work left to complete. In what time interval can each of them, working separately, complete the entire work?
## Solution.

Let the 1st worker can complete the entire job in $x$ hours, the second - in $y$ hours.

Productivity of the 1st: $\frac{1}{x}$, the second $-\frac{1}{y}$.

According to the condition $\left\{\begin{array}{l}\frac{1}{x} \cdot 2+\frac{1}{y} \cdot 5=\frac{1}{2}, \\ \frac{1}{2}+\left(\frac{1}{x}+\frac{1}{y}\right) \cdot 3=1-0.05,\end{array}\right.$ from which $x=12$ hours; $y=15$ hours.

Answer: 12 and 15 hours.