text: We should begin by expressing the distance D between them in terms of the elasped time T.\n\n(200-32T)^2 + (24T)^2 = D^2\n\nSince we are only interested in the rate of change of distance, we don't need to solve for D. We just differentiate the whole equation.\n\n2*(200-32T)(-32) + 2*(24T)(24) = 2D\n\nd/dt (D) = (-6400 + 1024T + 576 T)/D = (1600T - 6400)/D\n\nAt 6:00 pm the elasped time T is 6 hours.\n\nThe total distance D is sqrt[(200-32*6)^2 + (24*6)^2]\nD = sqrt[8^2 + 144^2] = sqrt(20800) = 144.22 km\n\nThe rate of change is (1600*6-6400)/144.22 = 22.2 km/hr