13.419 Two trains, 490 m and 210 m long, are moving towards each other at a constant speed on parallel tracks. The driver of one of them noticed the oncoming train at a distance of $700 \mathrm{~m}$; after this, the trains met after 28 s. Determine the speed of each train, given that the first train takes 35 s longer to pass a signal light than the second.
Solution. Let $x$ and $y$ be the speeds (m/s) of the trains. According to the first condition, $700=28(x+y)$. According to the second condition of the problem, $\frac{490}{x}-\frac{210}{y}=35$.

In the end, we have: $\left\{\begin{array}{l}x+y=25, \\ \frac{14}{x}-\frac{6}{y}=1\end{array} \Rightarrow\left\{\begin{array}{l}x=10, \\ y=15 .\end{array}\right.\right.$

Answer: 36 km $/$ h, 54 km $/ h$.