The Fly and The Trains Puzzle - Solution

The Puzzle:

The Fly and The Trains
Two trains are 200 km apart, heading towards each other, going at 50 km/hour each.

From one train a fly takes off, flying straight above the rails to the other train at 75 km/hour, bounces off it and flies back to the first train.

This is repeated till the trains crash together and the fly is smashed (Headline: Fly Dies in Freak Train Crash, Rest Survive)

What distance does the fly fly until its tragic end?

Note: there is a complicated and an easy way to solve this one.

Our Solution:

The complicated way: figure out how long its first journey is, then the return journey, and so on . . . .

Or simply figure that the trains will meet each other in 2 hours (200 km, and each is going at 50 km/hour), so the fly is flying for 2 hours at 75 km/h for a distance of 150 km.
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