[maest]

Indeed, doing the infinite sum is the "hard" way.

The easier way is to notice that the trains will collide in 1h and the fly will be constantly be flying at a speed of 60mph for the entire time. So the fly will travel 60 miles in the alloted time.

[cloudyhug]

It means I actually made a mistake! I understand your solution. :)

[dmurray]

Yeah, the distance changes by a factor of 1/3 each time (which actually makes for an easier infinite sum), not 2/3.