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
I quote form:
"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 
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]"
 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?