[QUOTE=BayleDomon]
I don’t know if Plynck reproduced the actual question with the correct numbers, but it may be that the actual question had slightly different numbers. Plynck’s numbers indicate the two trains meet just a little over two hours (assuming I calculated it correctly), and it’s possible that the numbers on the actual test were designed to make them meet in 2.5 hours. Regardless, I think that the trains wind up being irrelevant to the question; all that needs be known is that the bird is flying at a constant rate of 60 mph for 2.5 hours.
[/QUOTE]
The version I’ve seen (this one being a dog running back and forth between two people walking towards each other) is supposed to be easy in that you don’t have to compute the dog’s traveled path as a sum of decreasing-length zigs and zags (hard!), you just compute the time needed for the pedestrians to meet (easy) and use the dog’s known speed to get the distance traveled (also easy).
(The urban legend has someone posed this question to von Neumann, who (of course) came up with the answer in mere seconds. On being congratulated on seeing through the trick - “most people think they need to sum an infinite number of path segments”, he’s rumored to have said “But that’s what I did!”.)
My favourite version of that story is the Swedish math professor, whose first thought was “But - won’t we end up with a rotating dog?”.