13.033. Each of the two typists retyped a manuscript of 72 pages. The first typist retyped 6 pages in the same time it took the second to retype 5 pages. How many pages did each typist retype per hour, if the first finished the work 1.5 hours faster than the second?
Solution.

Let $x$ pages per hour be the typing speed of the first typist, then the second typist's speed is $\frac{5}{6} x$. The first typist worked $\frac{72}{x}$ hours; the second - $\frac{72}{5}$ hours. According to the problem, $\frac{72}{x}=\frac{72}{\frac{5}{6} x}-1.5$, from which $x=9.6($ pages/hour); the second typist typed $\frac{5}{6} \cdot 9.6=8$ pages/hour.

Answer: 8 and 9.6 pages/hour.