deanMonisLea
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At noon, ship A is 20 miles due west of ship B. Ship A is sailing west at 24 mph and ship B is sailing north at 23 mph. How fast (in mph) is the distance between the ships changing at 3 PM?

Verified Answer :

caylus

Hello,

I don't know how you solve this,
this is my resolution:

Let's e = the distance (in miles) between the 2 ships in function of t(time in  hour)

\(e= \sqrt{(20+24*t)^2+(23*t)^2} =\sqrt{1105t^2+960t+400}\\\\ v=\dfrac{de}{dt} = \frac{2*1105*t+960}{2* \sqrt{1105*t^2+960*t+400}} \\\\ if\ t=15\ then\ v=\dfrac{2*1105*15+960}{2*\sqrt{1105*15^2+960*15+400}} \\\\ =33.22945583.... ( \frac{mi}{h} )\)

The distance between the ships changing at 3 PM is 33 mph fast. I am hoping that
this answer has satisfied your query and it will be able to help you in your
endeavor, and if you would like, feel free to ask another question.

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