An oil tanker travels at a constant speed ( S meters per hour ), on a calm ocean, along a straight path. The shape of the tanker is a rectangle - W meters wide and L meters long capped by two semicircles at the bow and stern.

A patrol boat "circles" the tanker looking for any oil leaks. The patrol boat goes up the port side, across the bow, down the starboard side, and across the stern, and keeps cycling like this over and over. Relative to the ocean, the path of the patrol boat is always parallel to or perpendicular to the path of the tanker. During a cycle, the patrol boat makes four and only four turns. The speed of the patrol boat is twice the speed of the tanker.

Compared to the tanker, consider the patrol boat as a point; that its turns are instantaneous; and for safety it must maintain, at a minimum, C meters between itself and the tanker.

What is the shortest amount of time for the patrol boat to complete one cycle around the tanker in terms of C, L, S, and W?

(In reply to re(2): solution - relativity by brianjn)

I think Harry's point is valid.

When the patrol boat is traversing right to left, the tilt of the short side will be in one direction, but when it's left to right it will be in the other direction. Having opposite slopes means a trapezoid (to use the American term) will be formed, rather than a parallelogram.

Posted by Charlie on 2009-10-24 11:48:21