Santos-Dumont: Flying Balloon Puzzle - Solution

The balloon travels five miles in ten minutes with the wind, but requires one hour to go back to the starting point against the wind.

In 10 minutes it would travel 5/6 miles against the wind.

So, in 20 minutes it would travel 5+5/6 miles in calm, without any wind i.e. it would take 20x6/35x10 minutes i.e.34 minutes 17 and 1/7 seconds to go the whole ten miles in a calm, without any wind.