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'An Unhappy End' printed from http://nrich.maths.org/

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Two engines are 1000 metres apart at the ends of a single track railway line.

They set off towards one another at 10 metres/second.

Just at that moment, a fly sitting on the front of one of the engines sets off and starts to fly along the railway line at 25 metres/second.

The fly eventually meets the front buffer of the other engine which by now has travelled some way along the track.

The fly immediately turns round and flies at its usual speed towards the first engine.

When it gets there it turns round again and flies back towards the other engine, and so on, and so on...

How far will the fly have travelled before the unhappy end?

 

Extension:

Can you alter the distance or the speeds to change the problem?