13.284. Find the speed and length of the train, knowing that it passed a stationary observer at a constant speed for 7 s and spent 25 s to pass a platform of the same speed with a length of 378 m.
Solution.

Let $l$ be the length of the train, $V$ its speed.

According to the problem, we have the system

$$
\left\{\begin{array}{l}
7 V=l, \\
25 V=378+l,
\end{array} \text { from which } l=147(\mathrm{m}), V=21(\mathrm{m} / \mathrm{s})=75.6(\text { km } / \mathrm{h}) .\right.
$$

Answer: 75.6 km $/ \mathbf{h} ; 147$ m.