Brett happens to know a couple of aerospace engineers, and asked them about propelling yourself through space with a fart. Both Nate and Dan took the question completely seriously, and had a rather involved group text discussion on the many variables in the scenario. First they mused on how different flatulence would be in space compared to earth's air pressure and the restrictions of a space diet. The question of force was tabled because there is a limit to what the human body can do, and pivoted to how fast can you travel that one meter distance. Once the parameters were set, they went to work.
Thirteen minutes is a long time, but this is SCIENCE! However, astronaut Chris Hadfield addressed this years ago, and said it was pointless. Maybe that's because he was wearing pants at the time, and the original question assumes that the farting person is naked. Fart propulsion has been used for the plot of a movie, but as you might assume, it was a comedy. See the entire discussion at Imgur. And may the Force be with you.