Can somebody remind me of the solution to the following problem please?

Two trains are travelling along the same track towards each other, each travelling at 30 km/hr relative to the track. A bug starts off sitting on the front of one train, then flies to the other. As soon as it reaches the front of the second train, it immediately turns around and flies back to the first train. When it arrives there, it turns around and flies back again, and so on.

If the bug flies at 60 km/hr, how far does it fly before the two trains collide and the bug is squashed, given that the trains start 60 km apart?

Can somebody remind me of the solution to the following problem please?

Two trains are travelling along the same track towards each other, each travelling at 30 km/hr relative to the track. A bug starts off sitting on the front of one train, then flies to the other. As soon as it reaches the front of the second train, it immediately turns around and flies back to the first train. When it arrives there, it turns around and flies back again, and so on.

If the bug flies at 60 km/hr, how far does it fly before the two trains collide and the bug is squashed, given that the trains start 60 km apart?

It takes 1 hour for the trains to collide (60 km apart, 30 km/h each). Therefore the fly is flying for 1 hour total at 60 km/hr. So he goes 60 km.

A longer method is to add up the total distance the fly flies on each leg of his trip. You'll get a geometric series, easy enough to sum.

First time I did this problem (well, with bikes and slower speeds) I pretended one of the bikes were stationary.. found out how long it took for one bike to crash into the other one... then I got the flies speed. I read the problem in the book "A Beautiful Mind." In the movie towards the end you can hear him telling some students about the problem.

Thanks. I was looking for the quick solution.

There is as story about Von Neumann and this problem.

The problem was presented and Von Neumann came up with the solution in about 1-2 seconds. An astonished onlooker asked how it could be solved so quickly. The proproser of the problem explained the simple solution.

Von Neumann said "That is an easy way to solve it. I had to sum an infinite series."