13.395 A sportsman, walking along a highway, noticed that every 6 minutes a trolleybus catches up with him and every 3 minutes a trolleybus passes him in the opposite direction. Find the intervals at which trolleybuses depart from the terminal points and how many times slower the sportsman was walking compared to the trolleybus, assuming that trolleybuses depart in both directions at the same intervals, travel without stops, and maintain a constant and equal speed?
Solution. Let $x$ and $y$ be the speeds of the athlete and the trolleybuses, and $z$ be the interval of the trolleybuses' movement. Then $y z$ is the distance between the trolleybuses. According to the problem, $\left\{\begin{array}{l}y z=3(x+y), \\ y z=6(y-x),\end{array} \Rightarrow x=\frac{y}{3} ; z=4\right.$.

Answer: 4 min; 3 times.