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Math Help - Time Optimization, Single Variable Problem

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    Time Optimization, Single Variable Problem

    There is a lighthouse that is 4 miles from the closest point, B, on a straight beach. 4 miles east of B, is point C. If the keeper of the lighthouse can row his boat at 3 mi/h and walk at 5 mi/h (On a treadmill, I speedwalk at approximately 4.6 mi/h, so this guy must be pretty fit!). Find the distance between B and C he should land to minimize time taken.

    For this, I let x be the distance between B and D, the point where he would land his boat.
    The distance traveled across water would then be \sqrt{x^2+16}

    Wouldn't the equation be f(x)=3\sqrt{x^2+16}+5(4-x)=3\sqrt{x^2+16}-5x+20
    thus,
    f`(x)=\frac{3x}{\sqrt{x^2+16}}-5\\f`(x)=0;\5\sqrt{x^2+16}=3x\\25(x^2+16)=9x^2\\x=  \sqrt{-25}???
    So, I was wondering if this was just a faulty problem, if I messed up, or what. I feel like I overlooked something ridiculous.
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    Re: Time Optimization, Single Variable Problem

    Quote Originally Posted by ssgohanf8 View Post
    The distance traveled across water would be \frac{\sqrt{x^2+16}}{3}

    and f(x)=\frac{\sqrt{x^2+16}}{3}+\frac{(4-x)}{5}...
    Try in that way and do the subsequent calculations.

    dokrbb
    Last edited by dokrbb; April 9th 2013 at 11:14 AM.
    Thanks from ssgohanf8
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    Re: Time Optimization, Single Variable Problem

    Oh, haha. I figured that I was missing something ridiculous. The answer I was getting would have been a function of mi^2/h, I guess. Thanks, that really fixes/explains a lot.
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