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... I believe that if we restrict our attention to that question,
use the most common definition of work (the one that is presented in
introductory physics--i.e., work done = path integral of the applied
force dotted with the displacement of the point of application),
and
answer the question within the context of the introductory course, the
correct answer will be equal to the acquired bulk kinetic energy of
the anchor and the boat.
JD has suggested (correctly that the various parts of the boater do
work *on other parts of the boater*. That is, of course, correct.
But if one adds up all of *those* works (using the definition of work
given above) to get the "total work done by the boater", one will find
that the result is zero. This is because the work that any part a
does on any part b is necessarily equal and opposite to the work done
by part b on part a.