Provide an appropriate response.
-Suppose two automobiles leave from the same point at the same time. If one travels north at 60 miles per hour and the other travels east at 45 miles per hour, how fast will the distance between them be changing after three
Hours?
A) 75 mph
B) 50 mph
C) 125 mph
D) 150 mph

Question

Quizplus · Accepted Answer

The distance between the two automobiles can be found using the Pythagorean theorem, where the distance $d$ is the hypotenuse of a right triangle with legs of 180 miles (3 hours * 60 mph) and 135 miles (3 hours * 45 mph). Thus, $d = \sqrt{180^2 + 135^2} = \sqrt{32400 + 18225} = \sqrt{50625} = 225$ miles. Since this is the distance after 3 hours, the rate of change of distance is $225 miles / 3 hours = 75 mph$.

Provide an Appropriate Response