Puzzle: How fast are the trains?

3 05 2010

Two trains start at the same time, one from London to Liverpool, the other from Liverpool to Lon­don. If they arrive at their destinations one hour and four hours respectively after passing one anoth­er, how much faster is one train running than the other?

If you can solve this tricky puzzle explain your answer in the comments section below!

This puzzle was taken from “Amusements in Mathematics” by Henry Ernest Dudeny.

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2 responses

16 05 2010
Martin G

Let’s say the faster train is faster by a factor f. The slow train has so far covered a distance of d, the fast train a distance of f*d. Still to go: d for the fast train (in 1 hour), f*d for the slow train in 4 hours. Slow train travels f*d in 4 hours, so fast train would travel f*f*d in 4 hours, f*f*d/4 per hour. f*f*d/4 = d. So f=2, as f and d are positive.

16 05 2010
myownmathstutor

Fantastic explanation. Well done and congratulations! You were the first person to publish a solution!

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