Question

Car A is 30 mi apart from car b. Car A moves 30 mph due east at the same time car b moves 30 degrees south of east. how fast is the distance between them changing after an hour.

Answer 1

How are the two cars positioned relative to each other ?
e.g. is car A directly west of car B ?
is car A north of car B ?

Answer 2

I really don't know. We don't have any figure or anything. I just assumed there position in cartesian plane at (0,0) for Car B, and Car A at (30,0)

Answer 3

Ok, I will go with that assumption.
As I made my diagram, I also noticed that you did not state the speed of the car B.
I will also assume that the speeds are the same.

At a time of t hrs, let the distance between them be x miles

so by the cosine law:
x^2 = (30+30t)^2 + (30t)^2 - 2(30t)(30+30t)cos45°

then find dx/dt

Is there a typo in the last sentence?
"how fast is the distance between them changing after an hour." ?? , an hour ??? you mean 1 hour ?
if so, sub t = 1 to find x, then dx/dt