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

Let the time passes since noon be t hours
label the position of ship A as P, and that of ship B as Q
clearly PAQ will form a right-angled triangle, with AP=25t nautical miles and BQ = 22t nautical miles
Let the distance PQ = d

d^2 = (25t)^2 + (22t)^2 = 1109t^2
2d dd/dt = 2218t
dd/dt = 2218t/(2d) = 1109/d knots
when time is 6 pm, t = 6
d^2 = 1109(36)
d = 6√1109

dd/dt = 1109/(6√1109) = appr + 5.55 knots