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Hide and Seek at Sea

A destroyer division in attempting to intercept an enemy fleet approaching port A follows a plan called the "retiring search curve." This maneuver specifies that during daylight our destroyers steam toward the enemy position at maximum speed and, during darkness, turn and retire on the same course as the enemy at the enemy's maximum speed. This procedure is designed to prevent the enemy from passing through the scouting lines under cover of darkness.

Assume that such a maneuver was started at daylight 450 nautical miles from port A in a lattitude where there were 16 hours of darkness. Our destroyers reached a position 250 nautical miles from their starting point during daylight steaming, and at nightfall estimated the maximum enemy speed at 6 knots less than their speed. How far from Port A would our destroyers be at daybreak of the second day and what was the maximum speed of the two fleets?


Source: W.C. Eddy's Wartime Refresher in Fundamental Mathematics, 1945, p. 233-234