Oops, well this is embarrassing. I divided the wrong way. A loss of 39 pounds in 104 days amounts to only 0.4 lbs/day, not 2.7 lbs/day. Why didn't anyone catch this? Where were you DesertLili or chrisb1 when I needed your expert opinions? This clumsy error on my part means that my thesis about strenuous exercise losing weight faster than water-only fasting is completely wrong. It is just the other way around; water-only fasting would seem to be the fastest way to lose weight. It would take only 35 days to lose 39 pounds at a typical rate of 1.1 lbs/day. Too bad that fasting is not as much fun as hiking.
I would still maintain that three weeks (or maybe even 40 days as chrisb1 stated) is the upper danger limit for an unsupervised fast because of electrolyte depletion, liver and kidney stress and possible heart muscle attrition. These metabolic parameters should be observed closely during a long fast. Vigorous exercise may be less risky to lose a lot of weight but it will take longer.