Two trains, 100 miles part, are approaching each
other on the same track, each traveling 50 mph.
A bee, perched on the front of train A, begins to
fly at a speed of 75 mph toward train B; on
reaching train B, it reverses direction, always
flying at the same speed of 75 mph, until it once
more reaches train A, whereupon it again reverses
direction and flies toward train B, and so on.
How
far does the bee fly before it and the
two trains collide?
Solution to the Problem:
Because the trains are 100 miles apart and
are approaching each other at a relative velocity
of 100 mph, they will collide at the end of one
hour.
Since the bee is traveling at 75 mph for one
hour, it must travel 75 miles.
According to mathematical folklore, John von
Neumann was enjoying himself at a cocktail party,
when another guest proposed a similar problem to
him.
Von Neumann solved the problem
instantaneously by summing an infinite series in
his head!
He used the formula for the sum of
an infinite geometric series:
Sum = a1 / (1 - r)