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Math Help - related Rates problem

  1. #1
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    related Rates problem

    A bridge is 30ft above a canal. A motorboat going 10 ft/s passes under the center of the bridge at the same instant that a man walking 5ft/sec reaches the point. How rapidly are they separating 3 seconds later?
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  2. #2
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    Hello, ^_^Engineer_Adam^_^!

    This is a 3-dimensional problem.
    I hope I can explain it clearly.


    A bridge is 30ft above a canal.
    A motorboat going 10 ft/s passes under the center of the bridge
    at the same instant that a man walking 5ft/sec reaches the point.
    How rapidly are they separating 3 seconds later?
    Code:
                P   5t    A
                * - - - - *
                |
                |
             30 |
                |
                |
                * Q
               /
              /
          10t/
            /
           /
        B *

    At t = 0, the man is at point P.
    . . t seconds later, he has walked 5t feet to point A.

    At t = 0, the boat is at point Q.
    . . t seconds later, it has moved 10t feet to point B.


    The distance AB = z is the diagonal of a "box" with dimensions: 5t, 10t, and 30.
    . . . . . . . . . . . . ._________________ . . . .__________
    . . Then: . z .= .√(5t) + (10t) + 30 .= .√125t + 900


    Differentiate with respect to time and substitute t = 3.

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