Originally Posted by Ian
I asked this of my maths lecturer in uni. He took about ten seconds to mentally perform the calculation/integration. Can you beat his time?
Q.
A cyclist rides 100 miles from point A to point B at a constant velocity of 20mph. As he leaves point A, a bee on his handlebars flies ahead of him toward point B at a steady velocity of 25mph. When the bee arrives at point B it immediately returns to meet the cyclist somewhere in-between. The bee then flies at the same velocity in-between point B and the cyclist until the cyclist reaches point B.
What distance does the bee fly in total? (you have ten seconds)
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Spoiler
When the cyclist reaches point B, 5 hours will have passed. In those 5 hours the bee will have traveled 125 miles.
There's an interesting anecdote that goes with this puzzle. It was asked of the Mathematician John Von Neumann who pondered for a few
moments and answered it. The puzzler said "Oh, yo u know the trick." and Von Neumann replied "No, I summed the series.". I had tried to sum the series when I was in High School and didn't know how to do it. However, when I heard the anecdote, (and after I learned how to do it), I tried again to sum the series and found it rather easy. Of course, the trick answer is even easier.
