At noon, ship A is 180 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?

Answer 1

Distance square at time t after noon D² = (180 - 35t)² + 625t²; 2DdD/dt = 2(180 - 35t)(- 35) + 1250t

dD/dt = (2475t - 6300)/√(180 - 35t)² + 625t². If t = 4 h then dD/dt = 3600/√11600 = 33.43 km/h