Question

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 55mph.

How fast is the distance between the automobile and the farmhouse increasing when the automobile is 2 miles past the intersection of the highway and the road?


I don't even know where to begin, can someone PLEASE PLEASE PLEASE explain this step by step!

Thank you!!!!

Answer 1

as usual, begin by drawing a diagram. Clearly, the distance z is the hypotenuse of a triangle with sides 2 and 6.

Now, at time t hours from when the car passed the intersection, the distance z is

z^2 = (55t)^2 + 6^2
so, when the car is 2 miles past the intersection, t=2/55, and z=√40

2z dz/dt = 2(55t)(55)
2√40 dz/dt = 2(55 * 2/55)(55)
dz/dt = 17.38 mi/hr