13.082. Two groups of tourists must walk towards each other from tourist bases $A$ and $B$, the distance between which is 30 km. If the first group leaves 2 hours earlier than the second, they will meet 2.5 hours after the second group leaves. If the second group leaves 2 hours earlier than the first, the meeting will occur 3 hours after the first group leaves. At what average speed does each group walk?
Solution.

Let $x$ km/h be the speed of the first group, $y$ km/h be the speed of the second. If the first group starts earlier than the second, then $2.5 y + (2.5 + 2) x = 30$. If the second group starts earlier than the first, then $3 x + (3 + 2) y = 30$. Solving the system $\left\{\begin{array}{l}2.5 y + 4.5 x = 30, \\ 3 x + 5 y = 30,\end{array}\right.$ we find $x = 5$ km/h, $y = 3$ km/h.

Answer: 5 and 3 km/h.