Problem: Two Trains and a Fly

The Problem:

Two trains travel on the same track towards each other, each going at a speed of 50 kph. They start out 50km apart. A fly starts at the front of one train and flies at 75 kph to the front of the other; when it gets there, it turns around and flies back towards the first. It continues flying back and forth til the two trains meet and it gets squashed (the least of our worries, perhaps).

How far did the fly travel before it got squashed?

Attempt at a solution:

I can do this by summing the infinite series of the fly's distance for each leg. I get an answer of 37.5 km: but that's so nice! There must be a more intuitive way...is there?

-
fun fact: the story goes that Von Neumann was asked (a variant of) this problem, and responded with the answer almost instantly. The asker (Feynman or somesuch, I don't remember precisely) was impressed--he himself taken a long time to find the clever solution. Upon being asked how he did it, Von Neumann said "I summed the series!" – Jamie Banks Jul 24 '10 at 1:25
Actually, the anecdote is better than that: when Von Neumann produced the answer within seconds, the asker said something like "That was quick. You know, most people do this the hard way: by summing the series", to which Von Neumann replied: "What do you mean? That's how I did it." – Alex B. Jan 17 '11 at 4:25

1 Answer

The trains take half an hour to collide, which, at a rate of 75kph, leads to the fly travelling 37.5km.

-
oops, thanks Casebash...I've edited my answer to my own question so that it's correct... :heh: – Jamie Banks Jul 24 '10 at 1:35