"At 9am ship A is 50 km east of ship B. Ship A is sailing north at 40km/h and ship B is sailing south at 30km/h. How fast is the distance between them changing at noon?"
I never know how to set questions like this up!
It probably helps to sketch the ships.
The distance between the ships is a right triangle with one leg (the east/west leg) being a constant 50km and the other leg being the TOTAL distance traveled by both ships. Express the distance as a function of time then take the derivative with respect to time to find the rate of change of the distance at a given time.posted by Quidditch