13.298. Two athletes are running on the same closed track of a stadium. The speed of each is constant, but the first one takes 10 seconds less to run the entire track than the second one. If they start running from a common starting point in the same direction, they will meet again after 720 seconds. What fraction of the entire track length does each runner cover in one second?
Solution.

Let $V_{1}, V_{2}$ be the speeds of the athletes, $l$ be the length of the track. According to the problem, we have the system $\left\{\begin{array}{l}\frac{l}{V_{2}}-\frac{l}{V_{1}}=10, \\ 720 V_{1}-720 V_{2}=l,\end{array}\right.$ from which $\frac{l}{V_{1}}=80, \frac{l}{V_{2}}=90$.

Then the first athlete runs $\frac{V_{1}}{l}=\frac{1}{80}$ part of the length of the entire track per second, and the second athlete runs $\frac{\frac{l}{V_{2}}}{l}=\frac{1}{90}$.

Answer: $\frac{1}{80}$ and $\frac{1}{90}$.