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

We can use the Pythagorean theorem to find that the distance between the ships at noon is $\sqrt{(21t)^2+(15t)^2}=t\sqrt{621}$. Taking the derivative with respect to time, we get that the rate of change of the distance between the ships is $\sqrt{621}=11.14...$ miles per hour. Therefore, the correct answer is (C).

Two Ships Leave the Same Port at Noon