Trouble: 2 Trains and also a Fly

The Problem:

2 trains take a trip on the very same track in the direction of each various other, each addressing a rate of 50 kph. They start 50km apart. A fly begins at the front of one train and also flies at 75 kph to the front of the various other; when it arrives, it reverses and also flies back in the direction of the first. It proceeds flying back and also forth til both trains fulfill and also it obtains compressed (the least of our fears, probably).

Just how much did the fly traveling prior to it obtained compressed?

Try at a remedy:

I can do this by summing the boundless collection of the fly's range for each and every leg. I get a solution of 37.5 kilometres: yet that's so wonderful! There must be an extra instinctive means ... exists?