Help with a flat

I have a tight schedule on my way home, I leave work go home pick up my books for French class and I have about 5 minutes to eat something before heading to class. So when I went to leave yesterday and I had a rear flat on the fixie I figured I would be late for sure. I rolled the bike out of the garage so the garage attendant wouldn't try to help me. He knows nothing about bikes but is too chilvarous to let a woman work on a bike with a wrench. So I'm on the sidewalk changing the tire between the buidlings with 50 mph gusts of wind. The tire is really hard to change, it's is so fat that you can't get it between the rear breaks with out smashing to through un-inflated. I ride a fixie but I also have rear brakes for extra safety but this makes it tricky to line up the wheel right because the rear dropouts are horizontal. You have to put the chain around the gear pull back on the wheel and tighten with your wrench. Not hard if you have three hands! So I get it almost fixed and I'm at the hardest part which I always screw up and it's getting later. Then a messenger pulls up on a sweet Bianchi Pista (the same bike as my new track bike!) He had the wheel fixed on in about 30 seconds and I was on my way with the 50 mph tail wind at my back blowing me home. Nice! I wasn't even late for class afterall.