The squashed bee
Two trains set off from Oxford and London, a distance of 60 miles.
The trains are heading directly towards each other, each chugging
along at 60 mph. A bee is sitting on the front of the Oxford train
and flies at 120 mph to the front of the London train. It keeps
flying backwards and forwards between the two trains until they
collide and the bee is squashed.
The Puzzle: How far did the bee fly?
Hints and solutions below:
Hints will appear here!
If you have too much mathematical training, you may initially take an unnecessarily complicated approach. This problem requires only a very simple calculation.
Think about this question instead: how long does it take for the trains to meet?
The trains are heading to each other at a combined speed of 120 mph. At a distance of 60 miles, they take half an hour to meet. The bee is flying at 120 mph so the total distance it travels in half an hour is 120 × 0.5 = 60 miles.
The more complicated solution I alluded to in Hint 1 involves summing the infinite series of distances between each change of direction the bee makes.
A (probably apocryphal!) tale relates to an occasion when Norbert Wiener (a great mathematician at MIT) was told this riddle. Of course, Wiener came up with the solution immediately. The student who asked him the question remarked that when a mathematician is given the problem, he will usually solve it by summing the infinite series. To which Wiener replied, "Oh, I did."
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