B3. It takes one minute for a train travelling at constant speed to pass completely through a tunnel that is 120 metres long. The same train, travelling at the same constant speed, takes 20 seconds from the instant its front enters the tunnel to be completely inside the tunnel.
How long is the train?
Solution
Let $L$ be the length of the train in metres. It takes one minute for the train to pass completely through a tunnel, which is $120 \mathrm{~m}$ long. Therefore, in 60 seconds the train travels $(L+120) \mathrm{m}$ and its average speed is $\frac{L+120}{60} \mathrm{~m} / \mathrm{s}$. Travelling at the same speed, the train takes 20 seconds to travel $L \mathrm{~m}$. Hence,
$$
\frac{L+120}{60}=\frac{L}{20}
$$

Solving (1) gives
$$
\begin{aligned}
L+120 & =3 L \\
\text { so } L & =60 .
\end{aligned}
$$

Therefore, the train is $60 \mathrm{~m}$ long.