13.342. The distance between stations $A$ and $B$ is 360 km. At the same time, two trains depart from $A$ and $B$ towards each other. The train that departs from $A$ arrives at station $B$ no earlier than 5 hours later. If its speed were 1.5 times greater than it actually is, it would meet the second train earlier than 2 hours after its departure from $A$. Which train has the higher speed?
## Solution.

Let $V_{A}, V_{B}$ be the speeds of the trains departing from $A$ and $B$ respectively. According to the condition, we have the system

$$
\left\{\begin{array}{l}
V_{A} \leq \frac{360}{5} \\
\frac{360}{\frac{3}{2} V_{A}+V_{B}}180-\frac{3}{2} V_{A}$. At the maximum speed $V_{A}=72$ km/h, we have

$$
V_{B}-V_{A}>0 \text{, hence } V_{B}>V_{A} \text{. }
$$

Answer: the one departing from $B$.