Moscow Anthology/Amusing Problems/1

Problem

 * Two school students are observing a steam locomotive, the smoke from whose smokestack appears to be rising in a vertical plume.


 * As they have been taking meteorological measurements, they know that the wind is steady and gust-free, and its speed is $20$ miles per hour.


 * How do they know the train's speed?

Solution
As the smoke was rising vertically upwards, the speed of the smoke must have been $0$ relative to the wind.

Hence the smoke was travelling at the same speed as the wind.

Thus it must have been rising from a smokestack that is travelling at that same speed.

It follows that the train itself was travelling at $20$ miles per hour.