thanks for the inputs
Some erudite Archimedeans out there!
One part of the riddle was left out - did the anchor reach the bottom of the pond or not? Rivets picked up on this in his posting, where he assumed the anchor was on the bottom i.e. rope slack. I think this gives two solutions but it is beyond me to reason out.
This question was apparently used by one of the GEC managers in the 1960s when interviewing young prospective engineers for jobs - a rather tough one to encounter at a job interview.