[ [motion problem ]

A train passes by an observer in $t_{1}$ seconds, and at the same speed, it passes through a bridge of length $a$ meters in $t^{2}$ seconds.

Find the length and speed of the train.

#
In the second case, the train travels $a$ meters more, that is, it spends $t_{2}-t_{1}$ time on these $a$ meters. Therefore, its speed is $\frac{a}{t_{2}-t_{1}}$. In $t_{1}$ seconds, it covers a distance equal to its length, so this length is $t_{1}$ times the speed.

## Otвет

The length is $\frac{t_{1} a}{t_{2}-t_{1}}$, speed $-\frac{a}{t_{2}-t_{1}}$.

Note: The negative sign in the speed is likely a mistake in the original text, as speed is a non-negative quantity. The correct speed should be $\frac{a}{t_{2}-t_{1}}$.