Calculus Question!! PLEASE HELP ASAP SOS!

Question

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 20 knots. How fast (in knots) is the distance between the ships changing at 5 PM?

Answer 1

Place ship B at the origin and let y be its position, x be ship A's position. With x = -20 -25t and y = 0 + 20 t, distance between A and B comes from d² = (-20 -25t)² + (20t)² = 1025 t² + 1000 t + 400. Time derivative yields 2d d' = 2050 t + 1000, d' = (1025 t +500) / √ (d²). Knots are nautical miles per hour, so t = 5 and the rate at which distance is changing d' = 5625/176 = 31.9 knots at 5pm.