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### Two Trains And A Fly

Topic: g-rated

Two Trains And A Fly

Here's a puzzle for you, there's an easy way to figure it out, and a very difficult way. And probably a few medium ways somewhere in between. See which way you come up with.

1- Two trains 200 miles apart are moving toward each other;

2- Each one is going at a speed of 50 miles per hour.

3- A fly, starting on the front of one of them,

4- Flies back and forth between them at a rate of 75 miles per hour.

5- It does this until the trains collide and crush the fly to death.

6- What is the total distance the fly has flown?

The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances.

The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it.

ALPHA v0.3