I hope this doesn't remind you too much of the problems you had to work out in Grade 7. This one is a little different.
Two train engines are facing each other on a single track, two hundred miles apart. Simultaneously, they begin to move towards each other at 50 miles per hour (assume they don't have to take any time to get up to speed). Predictably, they crash.
At the outset, a little fly is sitting on the front of one of the engines. When the engines begin to move, the fly immediately takes off and flies towards the other engine. When it reaches the other engine, it turns around and returns to the first engine and so on, back and forth, to and fro, until the fly is crushed in the impact. (Tears.) Before the crushing, the fly flies at 75 miles per hour.
Question: How far does the fly fly before the impact?
PS: Puzzle is from What is the Name of This Book, by Raymond Smullyan (Prentice-Hall, 1978).