Okay, embarrassing story. Last time I changed a flat was on a local multi-user trail, but way out in the boonies where there wasn't much traffic.
My multi-tool has tire levers built in and this was the first time I'd tried to use them. It was a MAJOR PITA trying to manipulate the levers with the rest of the tool attached. After that experience I put some regular tire levers back in my seat pack, too bad about the extra space and weight.
Once I got the tire off, I totally could not find what caused the flat. It happened when I hit a bump so I thought it was a pinch flat, except the hole in the tube was extremely tiny. (When I got home and patched the tube later that day, only a slow stream of the tiniest bubbles came out of the hole when submerged in water. I'm actually surprised it went flat quickly, but I guess a high-pressure tube just doesn't get slow leaks.) So anyway I went over the tire two or three times trying to find what caused the puncture and never did.
Then I tried to use my CO2 inflater for the first time and totally could not get it to work. I still don't know why. DH and I actually burned a cartridge to find out what the problem was, and he could get CO2 out of it, but only a very, very weak stream, and it took pliers to get the cartridge off the inflater head.
So luckily I had the mini-pump I'd just bought. Very glad to have it, but it wasn't exactly a quick job.
I got the tire to where it was starting to get hard and saw that the bead wasn't properly seated. So I had to let out most of the air, squish the tire all around the rim, and pump it all over again.
Interspersed with all of this was swatting mosquitoes, since of course it was seemingly a freakin' swamp.
Some guy on a tri bike came by and asked if I needed help. I told him I was okay. After he'd gotten to the end of the trail and came back on his return trip (like, 14 miles) he asked me again. Same flat??? he asked incredulously
Thank goodness he was at least on a tri bike and appeared to know what to do with it, not some out-of-shape person on a 40 lb hybrid 
I had to look this up in my training log to see just how much time I'd taken. It was almost 45 minutes. Slowest. Tire. Change. Evah. And I'm an experienced rider who's changed many, many flats in my life (without exaggeration, back in the day I patched the holes by the side of the road, MUCH quicker that). Just never with a non-functioning CO2 inflater, stupidly designed tire levers or a weetie little mini-pump...
Speed comes from what you put behind you. - Judi Ketteler