Archive for the ‘Mathematics’ Category

Ran just over 3 miles today in about 36 minutes. Well, I ran 2 miles and ran/walked the last mile.

Have I mentioned that “I AM NOT A RUNNER? I think possibly so. Every time I go out to train for running I repeat this statement over and over to myself like a mantra. Well, it’s not so much that I consciously repeat the phrase but more like my brain spews it out in my head every time I take a step.

Now, not being a runner would not be an issue for most people. But, there is the slight problem that running is a part of every triathlon event and there is just no getting around it. I can’t claim ineptitude as a reason to be declared exempt from one-third of the events in a race I signed up for. So…I continue to train and slog along and punish myself and berate myself every step of the way.

Today as I went through this routine gathering data to submit to the “I Hate Running” website (there must be one of those, right?) I hit upon a more positive idea. My focus has been entirely too much on the running part and not enough on my real ultimate goal which is to complete an Ironman Tri within the allotted cutoff time. I’ll post more about the Ironman later, but for the running part suffice it to say that if I can complete the marathon part in around 5 hours, I’ll be doing dandy. I have a half-marathon race coming up on Dec. 7th in Tucson, so I thought I would do some calculations (being the math teacher and all).

Here are my assumptions:

  • Walking pace around 15 min/mile or 4 mph
  • Running pace around 10 min/mile or 6 mph
  • Goal for half-marathon total time is 2.5 hours
  • Distance is 13.1 miles

So, if I let w = walking time and r = running time, I get the handy dandy equations:

All this cool math (not high level at all but just kind of cool because I actually found a real-life example in my life of the use of a system two linear equations in two unknowns) provides the result that I need to walk for .95 hour and run for 1.55 hours. Since I need to break up the running and walking over the length of the race, I made a ratio of running to walking which is 1.55 hr: .95 hr. I can make this ratio into all sorts of equivalent ratios that give me lots of options for running and walking as follows:

  • 1.6 hr run: 1 hr walk
  • 48 sec run: 30 sec walk
  • 1 min 36 sec run: 1 min walk
  • 3 min 12 sec run: 2 min walk
  • 6 min 24 sec run: 4 min walk

So, you get the idea. Couple of things I need to test are that first, I can actually walk 4 mph as I am sure this rate will decrease as the miles increase and second, that I can run 10 mph (which does seem to be about my normal pace). But, at least I have some things to work with. A week from Sunday I have a Quarter Ironman coming up and would like to test the theory above and attempt to complete the running part (6.55 miles) in 1 hr 15 min. Given the ratios above, I should run 46.5 minutes at 6 mph pace and walk 28.5 minutes at 4 mph pace. This Sunday, there is a practice run at Tempe Town Lake. I think I will practice using the numbers above and report back.


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Survivor Math

Greetings! The following puzzle was part of the immunity challenge on Survivor last night:

Given the numbers 6, 1, 5, 4, 2, 7:
“The sum of both end values equals the sum of the middle two, the last is equal to the second minus the third and is only one less than its only neighbor.”

Want to take a stab at it? On Survivor, the professional video-gamer beat out the physics teacher to solve it.

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