Aroad perpendicular to a highway leads to a farmhouse located 55 mile away. an automobile traveling on the highway passes through this intersection at a speed of 60mph.60mph. how fast is the distance between the automobile and the farmhouse increasing when the automobile is 77 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.

The answer in this question is 44.7533 mphGiven information which we denote I as the distance of the automobile between the farmhouse, and S = the distance past the intersection of the highway and the road. 
Then I^2 = 5^2 + s^2. Taking the derivative of both sides of this equation yields 2I(ds/dt) = 2s(ds/dt), so (dl/dt) = s(ds)/I(dt). When the automobile is 7 miles past the intersection we have;dl/dt = 55√(7/5^2 +7^2) and gives us the answer of approximately 44.7533 mph