13.126. Two points rotate uniformly along two circles. One of them completes a full revolution 5 seconds faster than the other, and therefore manages to make two more revolutions in 1 minute. How many revolutions per minute does each point make?
## Solution.

Let the first point make a revolution in $x$ s; the second - in $x+5$ s. In a minute, the first point makes $\frac{60}{x}$ revolutions, and the second $-\frac{60}{x+5}$. According to the condition, $\frac{60}{x}=\frac{60}{x+5}+2$, from which $x=10$. The first point makes $\frac{60}{10}=6$ revolutions per minute, and the second $-\frac{60}{15}=4$ revolutions.

Answer: 4 and 6.