The HMS Dreadnaught is 40 miles north of Montauk and steaming due north at 20 mph, while the USS Mona Lisa is 50 miles east of Montauk and steaming due east at an even 30 mph. How fast is their distance apart increasing?
A)88 miles per hour
B)33 miles per hour
C)41 miles per hour
D)36 miles per hour
E)72 miles per hour

Question

Quizplus · Accepted Answer

The distance between the two ships can be found using the Pythagorean theorem: sqrt((40^2)+(50^2)) = 65 miles. The rate of change of distance between the two ships can be found using the Chain Rule:

d(distance)/dt = [(d/dt)(sqrt((40^2)+(50^2))]

Because the HMS Dreadnaught is traveling due north and the USS Mona Lisa is traveling due east, their paths are perpendicular and independent of each other. Thus, the rate of change of distance between them is simply the sum of their individual velocities:

d(distance)/dt = 20 mph + 30 mph = 50 mph

Therefore, the distance between the two ships is increasing at a rate of 50 mph, which corresponds to choice D.

The HMS Dreadnaught Is 40 Miles North of Montauk and Steaming