The mathematics of progress

I went out this morning with the PBA for their Saturday morning distance builder ride. By the time we headed out at 7am, there had been scattered [gasp!] rain showers in the area and ominous flashes toward the north, where the planned route would take us. Hoping avoid a dousing, we headed south and east instead—and promptly got soaked.

But that's not what this post is about. This post is about how a group of half a dozen of us got split from the main group at a traffic light and dropped. They didn't wait, but fortunately the area is part of many popular ride routes, so it wasn't a question of finding our way back. After a couple miles, I got antsy and upped my pace so that before long I was on my own. That made me paranoid about the traffic, which in turn made me up my pace again.

When I rolled into the parking lot with 51.75 miles and a rolling average of 16.5 mph on the computer, I was cooked. I headed over to Einstein's for the customary bagel, coffee, and post-ride visiting, during which one of the guys mentioned that we'd averaged 14.5 mph to the rest break. I said I thought that was at about 33 miles, if memory served, and my tablemates thought that was about right. That would mean that the second leg was 18.75 miles.

Now, about that algebra (Turtle! Look away!!). I was curious about my rolling average after we got separated from the group, so I trotted out the following equation:

(33 miles * 14.5 mph) + (18.75 * x)
----------------------------------- = 16.5 mph overall average
        51.75 miles total

...then...

(478.5) + (18.75 * x) = 853.875

...and...

18.75 * x = 375.375

...and finally...

x = 20.02

That's, ah say, that's miles per hour, boy.


Nah... that's got to be wrong. The data must be flawed.