Problem: Two Trains and a Fly

sequences-and-series

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?


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

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