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Math Help - Related Rates

  1. #1
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    Related Rates

    Two cars, A and B, are connected by a rope 39 feet long that passes over a pulley P. The point Q is on the floor 12 ft directly beneath P and between the cars. Cart A is being pulled away from Q at a sped of 2 ft/s. How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q?


    P distance from P to Q is 12 ft.
    / | \
    / | \
    / | \
    A Q B
    <-- <--


    I was able to use pythagorus to find the lengths of AP and PB when AQ=5 but and got 13 and 26 respectively.

    Let BQ=x and PQ=y and PB=z

    x^2 + y^2 = z^2

    2x dx/dt + 2y dy/dt = 2z dz/dt

    We know

    x=2root133
    y=12
    z=26

    dy/dt=0
    dx/dt= what we're solving for
    but what about dz/dt?

    Am I missing a step? Where did I go wrong?
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  2. #2
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    Re: Related Rates

    Wow. I apologize for the diagram above, it is not at all what I meant to represent.

    Think of it as a triangle with points ABP and Q as some point between A and B and PQ as a line splitting the triangle into two right triangles.
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