Running Pace

I'm running in a race in about a month. Its a half marathon, which is 13.1 miles. I think I can make it, but I'm not absolutely certain of that. Being in shape for a race is not really enough of a challenge for me. The only reason I'm doing it is for the scenery. It goes across the Golden Gate Bridge. Twice, in fact. So that will be an adventure in itself. I have run two other races in the past that are highlights in terms of the races themselves. One was in Knoxville, Tennessee that finished on the 50 yard line of the University of Tennessee stadium. The other was a half marathon in Indianapolis whose course included one lap (2.5 miles) on the Indy 500 track.

Anyway, on to math. Since I'm not 100% sure I can even finish, I'm definitely not sure what pace I should try to run. There was a predictor in my latest copy of Runner's World Magazine. They gave a way to predict your pace in various races by looking at times for shorter distances. I thought - good application.

The had predictors for the 5K, 10K, half marathon, and marathon. Since it applies to my situation, I'll just use the one for the half marathon.

• The Workout - "Race" a 10K at 80 percent effort. 
• The Formula - Take your 10K time in minutes (for example, a 55:30 is 55.5) and add 0.93. Multiply the result by 2.11.
• When - Three to five weeks before race day.
• Why - A 10K is great because it has that endurance aspect of a half marathon but doesn't require you to run too much so close to race day,

Yes, they could have condensed things quite a bit by using an equation rather than an explanation.

So the "formula" is f(x) =  2.11(x+0.93), 

To take their example of 55:30, you would have a half marathon time of f(55.5) = 2.11(55.5+0.93) = 119.067 minutes or 1 hour 59 minutes 4 seconds.

To put a little more algebra into this, we could say that we are hoping to run the half marathon in one hour 50 minutes. What kind of 10K would predict that kind of time?

Answer:  110 = 2.11(x+0.93), so  x = 51.203 or 51 minutes 12 seconds.

The other three races; 5K, 10K, and marathon; have different, but similar formulas, and would be great for Algebra I classes.