13.227. Two workers were assigned a task. The second one started working an hour later than the first. After 3 hours from the time the first one started, they had 9/20 of the entire work left to complete. By the end of the work, it turned out that each had completed half of the entire work. How many hours would each, working separately, need to complete the entire task?
Solution.

Let the 1st worker can complete the entire job in $x$ hours, the second in $y$ hours. The productivity of the 1st: $\frac{1}{x} ; 2$nd: $\frac{1}{y}$.

$$
\text { According to the condition }\left\{\begin{array}{l}
\frac{1}{x} \cdot 3+\frac{1}{y} \cdot 2=1-\frac{9}{20}, \\
\frac{x}{2}-\frac{y}{2}=1
\end{array} \text { from which } x=10 \text { hours, } y=8\right. \text { hours. }
$$

Answer: 10 and 8 hours.