Two ships leave the same port at noon. Ship A sails north at 21 mph, and ship B sails east at 15 mph. How fast is the distance between them changing at 1 p.m.?

Question

Quizplus · Accepted Answer

Let the distance between the two ships be denoted by d. Then, we can use the Pythagorean theorem to write:

d^2 = (21t)^2 + (15t)^2

where t is the time elapsed since noon. Taking the derivative of both sides with respect to t, we get:

2d(dd/dt) = 2(21^2)(1) + 2(15^2)(1)
dd/dt = (441 + 225)^(1/2) = 18.6 mph

So the distance between the two ships is changing at a rate of 18.6 mph at 1 p.m.

Two Ships Leave the Same Port at Noon