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At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
I keep getting 27.27 as the answer and and not sure what I am doing incorrect. 

Thank you!

az_lender2021-02-23T23:14:25Z

I'll pretend ship A is going east, it makes no difference.
r^2 =  (x+30)^2 + y^2 =>
2r dr/dt = 2(x + 30) dx/dt + 2y dy/dt.
Or, r dr/dt = (x+30) dx/dt + y dy/dt.
At 6 pm, x = 96, y = 144, and r = sqrt(126^2 + 144^2) = 191.34.
dr/dt = [(126)(16) + (144)(24)] / 191.34 
= maybe 28 knots, use a calculator !

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