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Here’s an interesting (and practical) problem given to me by my brother-in-law Steve Curtis, captain of the Capullo sportfishing boat out of Playa Tamarindo, Costa Rica:

Suppose your boat is anchored near the shore of a channel in which there is a steady current, and you are planning to run to a dock directly across the channel on the opposite shore. There are two ways one might steer the boat to the dock:

·    the crabbing method: steer a steady course with the nose of the boat pointed somewhat upstream, so the boat maintains a fixed orientation and crabs in a straight line across the channel

·   the pointing method:  keep the nose of the boat pointed directly at the dock

Which method  gets the boat to the dock faster, and by how much? (Assume the boat runs at a constant speed relative to the water, which is faster than the speed of the current relative to the shore.)