Calculus

A road perpendicular to a highway leads to a farmhouse located 6 mile away. An automobile traveling on the highway passes through this intersection at a speed of 75mph.

How fast is the distance between the automobile and the farmhouse increasing when the automobile is 10

miles past the intersection of the highway and the road?

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  1. if the car has gone x miles, the distance z to the farmhouse is

    z^2 = x^2 + 36

    so, find z(10) and then

    z dz/dt = x dx/dt

    and plug in your numbers.

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  2. h = highway distance from intersection

    d = auto-to-farmhouse distance

    by Pythagoras ... d^2 = h^2 + 6^2

    differentiating implicitly
    ... 2 d dd/dt = 2 h dh/dt

    dd/dt = h / d * dh/dt

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