A few years ago, after a tough day at work, I got passed by a couple of high-end road riders while I was commuting on my 1988 Specialized Hardrock with 1.5 slicks. It wasn't one of those "we just wanna get around you" passes, or so it seemed at the time. For whatever reason, right or wrong, I couldn't let go that they passed me, and chose to chase them.
For five miles I didn't give up, pushing 42/14 at a level nearly equal to whatever gearing they had. I just tucked my knees in toward the top tube and spun a faster cadence than I usually do. Oddly I didn't feel winded (I'm typically not a fast rider in any setting), and after another mile they both slowed down and let me go by. One quietly said, "nice pace" as I rode through.
Sure forgot about the bad day after that.