At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 20 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.)

Answer 1

A is west of B's northerly course
... distance is ... 50 + (7 * 25) = 225

B is north of A's westerly course
... distance is ... 7 * 20 = 140

the two courses form a right triangle
... with the distance (D) between the ships as the hypotenuse
... A^2 + B^2 = D^2

differentiating with respect to time (t) ... 2A dA/dt + 2B dB/dt = 2D dD/dt

dD/dt = [(225 * 25) + (140 * 20)] / √(225^2 + 140^2)