Somewhere on the high seas smuggler Stan is attempting, without much luck, to outspeed coast guard Charlie, whose boat can go faster than Stan's. Charlie is one mile east of Stan when a heavy fog descends. It's so heavy that nobody can see or hear anything further than a few feet. Immediately after the fog descends, Stan changes course and attempts to escape at constant speed under a new, fixed course. Meanwhile, Charlie has lost track of Stan. But Charlie happens to know Stan's speed, that it is constant, and that Stan is sticking to some fixed heading, unknown to Charlie.

How does Charlie catch Stan?

Charlie may change course and speed at will. He knows his own speed and course at all times. There is no wind, Charlie does not have radio or radar, there is enough space for maneuvering, etc.

x = Stan constant speed in miles                                             A = The starting point of Stan when the fog lifts                       y = time/60min, since the fog lifted

charlie will wait until x*y = 1, then he will head either clockwise or counter clockwise at the rate of x miles away from A per hour.

 

Posted by Sean on 2005-11-01 13:09:09