von Neumann and the "Fly and Train" Problem

Since this is a reformulation of the Fly and Train problem it might be

worth retelling the anecdote about Jonny Von Neumann's encounter

with it.

I quote form:

http://ei.cs.vt.edu/~history/VonNeumann.html

"One last anecdote about von Neumann's brilliant mathematical capabilities.

The von Neumann household in Princeton was open to many social activities

and on one such occasion someone posed the "fly and the train" problem [4]

to von Neumann. Quickly von Neumann came up with the answer.

Suspecting that he had seen through the problem to discover a simple

solution, he was asked how he solved the problem. "Simple", he

responded, "I summed the series!" [From Nick Metropolis]"

[4] Suppose two trains on the same track are 20 miles apart, heading

towards each other, each traveling at 20 miles per hour. Suppose a fly,

capable of flying at 60 miles per hour leaves the first train, flies to the other,

turns around and flies back and forth until the two trains collide. How far will

the fly travel before it is squashed between the crashing trains?

RonL