Question: Two ships leave port at the same time. One travels north at 80 knots (that is, 80 nautical miles per hour), and the other west at 80 knots. The distance between the ships increases at a constant rate. At what rate is the distance between the two ships increasing? 3. The attempt at a solution The distance traveled by the north bound ship = 80t [because distance traveled = speed x time taken] The distance traveled by the west bound ship = 80t Both leave port at the same time ... so they are making an ever increasing right triangle Let the distance between the boats at time t be d so d = √[(80t)² + (80t)²] d = √12800t² so dd/dt = 80sqrt(2) Why is this incorrect?