## 66. Math Puzzle $11 / 70$

On the cycling track, two riders are training. They ride at a constant speed. When they ride in opposite directions, they meet every 10 seconds. However, when they ride in the same direction, one overtakes the other every 170 seconds.

At what speed does each ride if the track length is $170 \mathrm{~m}$?
If the speed of the first driver is $x \frac{\mathrm{m}}{\mathrm{s}}$, then in 10 seconds he travels $10 x \mathrm{~m}$. If the second driver is driving towards him, in 10 seconds he covers the remaining part of the track $170-10 x \mathrm{~m}$. If the speed of the second driver is $y$, then this is $10 y$ m, i.e., $170-10 x=10 y$. If both are driving one behind the other, the first covers $170 x \mathrm{~m}$ in 170 seconds, and the second $170 y$ m, and if the first is faster than the second, then from one meeting to the next, the first covers one more lap, i.e., $170 x-170 y=170$.

Solving the system of equations yields $x=9 \frac{\mathrm{m}}{\mathrm{s}}, y=8 \frac{\mathrm{m}}{\mathrm{s}}$.