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.

Share this puzzle with your friends:

Bookmark and Share




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

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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: