A road perpendicular to a highway leads to a farmhouse located 9 mile away. An automobile traveling on the highway passes through this intersection at a speed of 45mph. 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?

27.63 mph

Step-by-step explanation:

First we find the distance, p between the Car and the house using Pythagoras theorem.

Taking derivatives of:

Since the farmhouse does not move, its speed

Therefore:

The distance between the automobile and the farmhouse is increasing at a rate of 27.63mph.

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.