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 May 26th, 2013, 05:22 PM #1 Newbie   Joined: May 2013 Posts: 3 Thanks: 0 Related Rates I've done this problem so many times and I don't understand what i'm doing wrong. The problem is... At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
 May 26th, 2013, 06:02 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,661 Thanks: 965 Math Focus: Elementary mathematics and beyond Re: Related Rates Let d(t) be the function of distance between the two ships in terms of t hours past noon: $d(t)\,=\,\sqrt{(25t\,+\,20)^2\,+\,(16t)^2}$ $d'(t)\,=\,\frac{2\,\cdot\,(25t\,+\,20)\,\cdot\ ,25\,+\,2\,\cdot\,(16t)\,\cdot\,16}{2\sqrt{(25t\,+ \,20)^2\,+\,(16t)^2}}\,=\,\frac{881t\,+\,500}{\sqr t{(25t\,+\,20)^2\,+\,(16t)^2}$ $d'(3)\,\approx\,29.53\text{ so the distance is increasing at a rate of about 29.53 knots per hour.}$

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