13.226. A manuscript of 80 pages was given to two typists. If the first typist starts typing the manuscript 3 hours after the second, then each of them will type half of the manuscript. If both typists start working simultaneously, then after 5 hours, 15 pages will remain untyped. How long will it take for each typist to type the manuscript individually?
Solution.

Let the first typist can retype the manuscript in $x$ hours; the second - in $y$ hours. The first typist prints one page in $\frac{x}{80}$ hours, the second - in $\frac{y}{80}$ hours. The work rate of the first: $\frac{80}{x}$ pages/hour, the second: $\frac{80}{y}$ pages/hour.

According to the condition: $\left\{\begin{array}{l}\frac{40 y}{80}-\frac{40 x}{80}=3, \\ \frac{80}{x} \cdot 5+\frac{80}{y} \cdot 5=80-15,\end{array}\right.$ from which $x=10$ hours, $y=16$ hours.

Answer: 16 and 10 hours.