13.311. Two trains, a passenger train and an express train, set off towards each other simultaneously from two points that are 2400 km apart. Each train travels at a constant speed, and at some point in time, they meet. If both trains had traveled at the speed of the express train, they would have met 3 hours earlier than the actual meeting time. If both trains had traveled at the speed of the passenger train, they would have met 5 hours later than the actual meeting time. Find the speeds of the trains.
Solution.

Let $V_{1}, V_{2}$ be the speeds of the passenger and express trains, respectively, and $t$ be the time of travel until the trains meet. According to the problem, we have the system $\left\{\begin{array}{l}t\left(V_{1}+V_{2}\right)=2400, \\ 2 V_{2}(t-3)=2400, \text { from which } V_{1}=60(\text { km } / \text{h}), V_{2}=100(\text { km/h). } \\ 2 V_{1}(t+5)=2400,\end{array}\right.$

Answer: 60 and 100 km/h.