C1. A train travelling at constant speed takes five seconds to pass completely through a tunnel which is $85 \mathrm{~m}$ long, and eight seconds to pass completely through a second tunnel which is $160 \mathrm{~m}$ long. What is the speed of the train?
Solution
Let the train have length $l$ metres.
When the train passes completely through the tunnel, it travels the length of the tunnel plus its own length.
Therefore the first fact tells us that the train travels $85+l$ metres in five seconds, and the second fact tells us that it travels $160+l$ metres in eight seconds.
By subtraction, we see that the train travels a distance of $(160+l)-(85+l)$ metres in $8-5$ seconds, that is, it travels 75 metres in 3 seconds, which corresponds to a speed of $25 \mathrm{~m} / \mathrm{s}$.