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Math Help - Help solving and reasoning a word problem.

  1. #1
    Ash
    Ash is offline
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    Help solving and reasoning a word problem.

    I need to know how to solve this problem. This is the information I was able to write down. Hopefully, someone has heard of it before and can tell me how to solve it.

    A priest takes a pilgrimage to a hill every morning. He steps on the path at 6:00 am and stays on the path until he reaches the top of the hill. Six hours later, he arrives and reaches the top of the hill at 12:00 noon.
    Then, he turns back and starts again, but at some point in the journey, he will reach a specific point at exactly the same time and same place both trips. What goes on from 6:00 am to noon time is up to the individual.

    How can this take place?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ash View Post
    I need to know how to solve this problem. This is the information I was able to write down. Hopefully, someone has heard of it before and can tell me how to solve it.

    A priest takes a pilgrimage to a hill every morning. He steps on the path at 6:00 am and stays on the path until he reaches the top of the hill. Six hours later, he arrives and reaches the top of the hill at 12:00 noon.
    Then, he turns back and starts again, but at some point in the journey, he will reach a specific point at exactly the same time and same place both trips. What goes on from 6:00 am to noon time is up to the individual.

    How can this take place?
    Let f(t).\ t \in [6,12] be the function giving the priests position as a function of
    time as he ascends, and g(t),\ t \in [6,12] be the corresponding function for
    the descent. These are both continuous functions taking values on the same
    interval, as is h(t)=f(t)-g(t) , but h(6)=0, and h(12)=0, so the Intermediate
    Value Theorem tells us that there is a time \tau \in (6,12) such that h(\tau)=0.

    RonL
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