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Math Help - Related Rate Problem

  1. #1
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    Related Rate Problem

    Hey Guys. I'm correcting a Math test for extra points right now and I came across a question that I can't seem to figure out how to solve.

    Anyone care to help?

    Heres the problem:

    A man 6 feet tall is walking at a rate of 5 ft/sec towards a light that is 20 feet above the ground. When he is 10 feet from the base of light, at what rate is the tip of his shadow changing.

    I know how to draw the picture and thats about it haha. Where do I start?

    Any help?

    Thanks!

    Aaron Snyder
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  2. #2
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    let x = distance man is from the light

    s = shadow length

    using similar triangles from your sketch ...

    \frac{20}{x+s} = \frac{6}{s}

    3x = 7s

    you know \frac{dx}{dt} ... find \frac{ds}{dt}

    rate that the tip is moving is \frac{d}{dt}(x+s)
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  3. #3
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    Thanks so much! I appreciate it! If only i had thought that the first time around! haha.
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  4. #4
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    Quick question,
    where did you get the 3x=7s from? I'm not seeing it right now.
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