Two Trains and a Fly

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).


Zootenany Hoodlum said...

too freaking far. should have just lazed about drinking a G and T, in my opinion.

Mr. Kite said...

Okay, I think the trains have two hours before they crash, and if the fly is flying at 75 mph, then the fly should cover 150 miles in the two hours before the crash.

This seems kinda easy to me, but I'm betting that I'm wrong in my reasoning somewhere.

Don't you Canadian types use the metric system? Why miles instead of kilometers? Geesh!

fiona-h said...

You are correct!! Some people would immediately start summing the series - but this is exactly the way to do it.

we're kinda half-hearted about the metric system...

richard said...

Like Mr. K said -- same method, but he has the honour.

Half-hearted about metric? I'd say we try to be bilingual but are tolerant of our weaknesses.