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Two cyclists, 120 miles apart, approach each other, each pedaling at 10 miles per hour. A fly starts at one cyclist and flies back and forth between the cyclists at 15 miles per hour. When the cyclists come together (and squash the fly between them), how far has the fly flown?

I know that I am supposed to find some sort of series here, but I don't really know how to approach this. How do I find the terms?

minjof32k
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    You actually don't need series at all! – Bolton Bailey Sep 26 '16 at 01:07
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    You don't need a series. It's a well known problem I think it would be a shame to reveal the trick to solve it easily. There is a story about John von Neumann being given this problem (or one very much like it) and immediately answering it. The asker says "oh wow you spotted the trick? Most people try to sum the series" to which von Neumann replied "what other way is there to solve it?" – Dan Robertson Sep 26 '16 at 01:10

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The cyclists approach each other at a combined speed of $20$ miles per hour, so they meet after $6$ hours. During all of this time the fly was travelling at a speed of $15$ miles per hour. Hence it travelled $90$ miles during these $6$ hours.

Asinomás
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This is actually a famous question which can be answered in two ways. One way is a series the other way is by the above answer.

video of what's called the train-bird problem

https://www.youtube.com/watch?v=kKMBjlIwU2k

John Murphy
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  • While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review – Joey Zou Sep 26 '16 at 01:57
  • I didn't downvote your post. However, you may wish to add more details to your answer, such as explaining what "One way be a series" means. As it stands, your answer contains little useful information. – Joey Zou Sep 26 '16 at 02:18
  • accidentally put be instead of is. My comment doesn't provide any useful information but the video does. I could have just said everything in the video but that would have taken a lot of time and would have been no more useful to the guy who wrote the question. Sorry for accusing you of stuff you didn't do. I'm really new to this. – John Murphy Sep 26 '16 at 02:57