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Math Help - Flight distance

  1. #1
    Site Founder MathMan's Avatar
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    Flight distance

    Two people live 20 km from eachother. They start cycling towards eachother with a speed of 10 km/h. A fly starts from one of them and flies to the other person and then back to the first person. It has an average speed of 15 km/h. It continues to do this until the two people meet. How far will the fly have flown when the two people finally meet? Apparently this has one very complex solution as well as being a simple grade school/high school problem, but I'm having trouble seeing the simplicity I think...anyone?
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  2. #2
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    I think this is an old, and popular, puzzle.

    The key is the total time of the fly in flying.
    Here the average speed it flies is 15 km per hour. So if the fly flew in one hour altogether, back and forth, then the fly would have flown 15 km.

    The fly flies until the two people meet.
    The two people are 20 km apart. They drive towards each other at 10 km per hour each.
    So when they meet, how many hours elapsed?
    Without using formulas, they meet after 1 hour. (Each one covers 10 km when they meet. Their speed, each, is 10 km per hour, so, they drive for one hour only until they meet.)

    That means the fly flies in one hour only, for whatever number of turnings it has to do.

    So, the fly would have flown 15 km when the two people meet.

    ------------
    Like I said, your question is an old and popular puzzle. I take no credit from giving this answer. I just pass it around.
    Last edited by ticbol; April 13th 2005 at 05:55 AM.
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  3. #3
    Site Founder MathGuru's Avatar
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    It would be intersting to figure out how many times the fly turns around?

    Can anyone do it?
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  4. #4
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    Teal: Bikers paths
    Red: Fly path

    At least 2 turns. There might be a 3rd turn.
    Attached Thumbnails Attached Thumbnails Flight distance-flybike.png  
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  5. #5
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    On second thought, if the fly does not pause for any time, it turns infinitely many times.
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  6. #6
    Site Founder MathMan's Avatar
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    Thanks ticbol,

    I see it now.
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