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Math Help - Quickest Route

  1. #1
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    Quickest Route

    Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2mph and walk 5mph. Where should she land her boat to reach the village in the least amount of time?

    I've never done optimization using time before. Any help is appreciated, thanks.
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  2. #2
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    Quote Originally Posted by lancelot854 View Post
    Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2mph and walk 5mph. Where should she land her boat to reach the village in the least amount of time?

    I've never done optimization using time before. Any help is appreciated, thanks.
    make a sketch.

    you want to minimize time ...

    time = distance/rate

    \displaystyle t = \frac{\sqrt{2^2 + x^2}}{2} + \frac{6-x}{5}

    find \frac{dt}{dx} and minimize.
    Last edited by skeeter; November 30th 2010 at 05:21 PM. Reason: fix typo
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    May I just ask where the 4 came from? Everything else is understandable, thanks for the help.
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  4. #4
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    Quote Originally Posted by lancelot854 View Post
    May I just ask where the 4 came from? Everything else is understandable, thanks for the help.
    should be 5 for the speed on land ... my typo.
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