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Math Help - Mathyiscs Problem

  1. #1
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    Mathyiscs Problem

    Joe and John are friends, and they are living 60 km from each other (one of them in Nadi and the other in Sigatoka). One day they decide to meet, when they ride their bicyclesthat afternoon. They leave their own towns in the same time (after the afternoon tea), when a butterfly sits onto Joe's nose. Joe tries to catch it, but it can escape. Then the butterfly flies onto John's nose who is on his way to meet his friend. He also tries to catch the butterfly who turns back to Joe immediately. It continues to fluctuate between the two riding friends, till they can finally smash it when they meet. They are wondering how long the route of the butterfly's last challenge was in kilometer from Joe to John, plus from John and to Joe...etc..till it died. Can you calculate it? (Assume the speed of each of the bicyclists was 10 km/h and the butterfly could fly 20 km/h.)
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  2. #2
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    Hello, Karlos!

    This is a classic (very old) problem ... with a simple solution.


    Joe and John are friends, and they are living 60 km from each other.
    One day they decide to meet, when they ride their bicycles that afternoon.
    They leave their towns at the same time and a butterfly sits onto Joe's nose.
    Joe tries to catch it, but it flies to John's nose who is on his way to meet his friend.
    He also tries to catch the butterfly who turns back to Joe immediately.
    It continues to fluctuate between the two riding friends till they meet.

    Find the total distance that the butterfly flew.
    (I think that's is what was asked; the wording is terrible.)
    Assume the speed of each friend was 10 km/hr and the butterfly's was 20 km/hr.

    Joe and John are approach each other at a combined rate of 20 km/hr.
    It will take them 3 hours to cover the 60 km.

    At 20 km/hr, in 3 hours, the butterfly travels: . 20 \times 3 \:=\: 60 km.

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  3. #3
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    Mathysics Problem

    Thanks mate! appreciate your help.
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  4. #4
    Moo
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    Hello,

    Another way of seeing it :
    The 2 boys will meet after 30km. They'll stop at this moment.
    Since the butterfly is twice as fast as the boys, it will travel twice their distance in the same time. So the answer is 30 \times 2=60 \text{ km}

    See ? No need to go through the intermediate step of knowing the duration of the travel. No need either to know their exact speed, only the ratio.
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