# Calculus - Related Rates

A road perpendicular to a highway leads to a farmhouse located 5 miles away. An automobile traveling on the highway passes through this intersection at a speed of 65mph.

How fast is the distance between the automobile and the farmhouse increasing when the automobile is 1 miles past the intersection of the highway and the road?

The distance between the automobile and the farmhouse is increasing at a rate of _______ miles per hour

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1. Let the distance on the road be x. Then the distance z to the house is

z^2 = x^2+25
z dz/dt = x dx/dt
z(1) = √26

√26 dz/dt = 1 * 65

...

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