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Math Help - Optimization problem #4

  1. #1
    MHF Contributor alexmahone's Avatar
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    Optimization problem #4

    A small island is 2 km off shore in a large lake. A woman on the island can row her boat at 10 km/h and can run at a speed of 20 km/h. If she rows to the closest point on the straight shore, she will land 6 km from a village on the shore. Where should she land to reach the village most quickly by a combination of rowing and running?
    Last edited by alexmahone; July 23rd 2010 at 02:55 AM.
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    You need to draw a picture for this to understand it completely.

    You need to minimise a function of time as a combination of running and rowing.

    I.e f(x) = Runing Time + Rowing Time.

    I get f(x) = \frac{6-x}{20}+\frac{\sqrt{x^2+2^2}}{10}

    Then solve for f'(x) = 0
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