A straight driveway perpendicular to a straight highway leads to a house located one mile away. A truck travels past the house traveling 60 miles per hour. How fast is the distance between the truck and the house increasing when the truck is three miles past the intersection of the highway and road

Answer 1

let the truck' distance from the intersection be x miles

make a diagram and you should have a right-angles triangle with sides x,1, and let the hypotenuse be y

given dx/dt = 60 mph
find dy/dt when x = 3

y^2 = x^2 + 1
2y dy/dt = 2x dx/dt

dy/dt = (x dx/dt)/y

when x = 3, y = √10
dy/dt = 3(60)/√10 = appr. 56.92 mph