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  1. #1
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    related rates

    Two boats are headed due north. Boat A is traveling at 25 ft/sec while Boat B is traveling at 15 ft/sec. Boat A is following a course which is 240 ft west of boat B. How fast is the distance between the boats changing when Boat A is 450 ft behind Boat B?
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  2. #2
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    Problems like this call for ol' Pythagoras.

    The boats are 240 feet apart. That is constant. Therefore, dx/dt=0

    One is travelling at 25 ft/sec and the other at 15 ft/sec. 25-15=10

    dy/dt=10 ft/sec.

    D^{2}=x^{2}+y^{2}

    When x=240 and y=450, then D=510

    Differentiate:

    D\frac{dy}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}

    (510)\frac{dD}{dt}=240(0)+(450)(10)

    \frac{dD}{dt}=\frac{150}{17} \;\ ft/sec

    Check my figures. I have done this in a hurry.
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