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A road perpendicular to a highway leads to a farmhouse located 8 mile away.An automobile travels past the farmhouse at a speed of 80 mph.

How fast is the distance between the automobile and the farmhouse increasing when the automobile is 7 miles past the intersection of the highway and the road?

The distance between the automobile and the farmhouse is increasing at a rate of ___________ mph.

  • math -

    Let the distance from the sideroad be x miles, let the distance between the car and the house be y miles.
    You have a right-angled triangle where
    x^2 + 8^2 = y^2

    then 2x dx/dt = 2y dy/dt (1)

    when x=7, y^2 = 49+64 = 113
    so when x=7, y= √113 and dx/dt = 80

    sub these values into equation (1) and solve for dy/dt

  • math -

    52.68 mph

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