Expert: Ahmed Salami - 2/13/2010

Question
Sir, i need help on this problem. I have no idea what they are asking and this is all of it on the word problem.

Two cars travel at the same intersection at the same time. One car is traveling due north at the speed of 40mph. The second car is traveling due east at 50mph. At what speed, in mph, is the distance between two cars changing after two hours?

Answer
Hi Austin,
Taking the intersection as reference, the distance between the two cars at any time is the hypotenuse of the right-angle triangle formed with the car distances to the north and east.
After t hours, the car travelling north has moved a distance of 40t miles and the other car has traveled 50t miles. The distance between them at this time is
D = √[(40t)² + (50t)²]
 = √[1600t² + 2500t²]
 = √[4100t²]
 = 64.03t
The rate of change of this distance is
dD/dt = 64.03 mph
and we can see that it is constant and doesnt depend on the value of t.

Regards