Do’s and Don’ts: How to Meet Men on the Trail
By: Amy Baker
You are running the 4 mile congress loop at Town Lake. Will you see more men on the trail if you run at a 7min/mile pace, or a 9min/mile pace?
Assume that the number of men on the trail is constant (as one leaves another starts). Assume they are about evenly spread out, the same number run counterclockwise as run clockwise, and they are all running the 4mile loop. Assume all men are running around 8:00 pace.
See the end of this blog for the answer.
On Valentine’s Day and I am out for an easy run, feeling a little spiteful of men at the time. I finish up the 10-mile loop at Town Lake and a sorta fast/sorta cute member of the evil sex turns the corner in front of me. Just as I’m considering catching up and trying to talk to this guy, Beyoncé’s “Single Ladies” comes on my ipod. All the energy and frustration of my former relationship comes into my head and I’m pumped. The poor guy is no longer a target, but an innocent victim (well not really, since NO man is ever really innocent). Halfway through the song I pull up next to him, mutter “hi”, and flash a quick smile that says, Honey, you don’t stand a chance. Beyoncé keeps singing and I quietly blow by him, controlling my breathing as to not seem tired. Half-mile later is the end of the loop, I stop, and think maybe I was too hard on him; I really could use a date … it’s been a while. He should be here any second and I could at least talk to the guy like a “mature adult”. A few minutes later, he is still nowhere to be seen. The guy turned around? Maybe? I guess blowing by good-looking men is NOT the way to find yourself a date… it still is really fun though.
This really got me thinking. I probably see more men on the trail than I see anywhere else in one day. It brought me to our leading question.
Solution: The 9min/miler since the number of men you see is proportional to time spent running and NOT your pace.
Explanation: The 9min/mile runner and the 7min/mile runner will see the SAME number of men who are running the SAME direction as them. The 7min/mile runner will catch anyone who started less than 4minutes before them; the 9min/mile runner will be caught by anyone who started less than 4minutes after them. Since we are assuming the number coming and going is constant and they are evenly distributed this is the same. On the other hand, we need to consider men going in the OPPOSITE direction. Running the 4mile loop at 7min/mile takes 28 minutes, running at 9min/mile takes 36 minutes. The men running at 8min/mile will take 32 minutes. The 7min/miler will see all the ones on the trail running the opposite direction plus any who start to run the opposite direction in the next 28minutes. The 9min/miler will see all the men running the opposite direction on the trail plus any who start in the next 36 minutes. Since more men will start in the next 36 minutes than the first 28 minutes, you will see more men if you take longer to run the loop. Thus the 9min/miler will see more men.
This question is similar to this question: will you get more wet if you run in the rain or walk in the rain? Since there is rain everywhere, it doesn’t matter if you are running or walking, the same amount of rain/minute hits you. However since walking takes longer than running when traveling a set distance, you will get wetter walking in the rain. In this case, I guess, it’s raining men? Keep reading next time for more math questions about running.