# Math

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 22 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

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1. Did you make a diagram?
Let the time passed since noon be t hours
so the distance covered by ship B since then is 22t, and the distance covered by A since noon is 16t
Let the distance between the ships be D
I see a right-angled triangle where
D^2 = (16t+30)^2 + (22t)^2
2D(dD/dt) = 2(16t+30)(16) + 2(22t)(22)
dD/dt = (740t+480)/D

at 7:00 pm, t = 7 and
D^2 = 43880
D = √43880 = 209.476
and
dD/dt = (740(7)+480)/√43880 = 27.02 knots

check my arithmetic, I tend to make errors so early in the morning before my third cup of coffee.

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2. The answer is correct. Thank u for ur help.

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3. Thank you very much for your help. everything makes sense and I got 100% on my answer.

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