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Math Help - word problem about time and distince

  1. #1
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    Post word problem about time and distince

    mike and john are in boats located at the center of a lake. At time t=0, Sonya begins travelling south at a speed of 36 mph. At the same time, Isaac takes off, heading east at a speed of 27 mph. How fast is the distance between them changing after 12 minutes?
    Last edited by lsanger; April 22nd 2010 at 02:58 AM.
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  2. #2
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    Quote Originally Posted by lsanger View Post
    Sonya and Isaac are in motorboats located at the center of a lake. At time t=0, Sonya begins travelling south at a speed of 36 mph. At the same time, Isaac takes off, heading east at a speed of 27 mph. How fast is the distance between them changing after 12 minutes?
    let y = distance traveled south
    x = distance traveled east
    z = straight-line distance between the two boats

    given \frac{dx}{dt} and \frac{dy}{dt} ... question asks for \frac{dz}{dt} after 12 minutes = (0.2 hr)

    z^2 = x^2 + y^2

    take the time derivative, calculate x, y, and z for t = 12 minutes and solve for \frac{dz}{dt}
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