Related Rates?

Question

At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship B is sailing north at 25 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.)

Answer 1

Initially distance between ships is 30 nautical miles.
The distance between the ships as a function of time is
D = sqrt((20 + 22t)^2 + (25t)^2)
= sqrt(400+ 440t+ 484t^2 +625t^2)
= sqrt(1109t^2 +440t + 400)
dD/dt = ((2218t+440)/(2(1109t^2 +440t +400)^.5
When t = 6,
dD/dt = (2218*6 +440)/(2(1109*36 +440*6+400)^.5
dD/dt = 32.2knots