13.216. Two motorcyclists set off simultaneously towards each other from points $A$ and $B$, the distance between which is 600 km. While the first covers 250 km, the second covers 200 km. Find the speeds of the motorcyclists, assuming their movements are uniform, if the first motorcyclist arrives at $B$ 3 hours earlier than the second at $A$.
Solution.

Let $x$ km/h be the speed of the first motorcyclist; $y$ km/h be the speed of the second. The first covers 250 km in $\frac{250}{x}$ h; the second covers 200 km in $\frac{200}{y}$ h. According to the condition, $\frac{250}{x}=\frac{200}{y}$.

The first arrives at $B$ in $\frac{600}{x}$ h; the second arrives at $A$ in $\frac{600}{y}$ h.

According to the condition, $\frac{600}{x}+3=\frac{600}{y}$.

Solving the system $\left\{\begin{array}{l}\frac{250}{x}=\frac{200}{y}, \\ \frac{600}{x}+3=\frac{600}{y},\end{array}\right.$ we find $x=50$ km/h, $y=40$ km/h.

Answer: 40 and 50 km/h.