Moscow Anthology/Amusing Problems/1
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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.
$\blacksquare$
Sources
- 1972: Boris A. Kordemsky: The Moscow Puzzles: 359 Mathematical Recreations ... (previous) ... (next): $\text I$: Amusing Problems: $1$. Observant Children