MILES THIS WEEK: (Many)^3
WHERE TO: Everywhere.
This all started in my high school running days, when I was a part of Podunk Iowa High School’s “Magnificent Seven” — the track team being unpopular exclusive enough to only have seven women on it. As the resident distance runner, I ran the 3000, the 1500, and the 800. And with each lap, I ran by Coach P., who would wail, stopwatch in hand as I blew by his corner of the track,
“DJ YOU GOTTA GOOOOOOO!”
…and then he would go back to his nervous pacing and nail-chewing until I came back.
“YOU GOTTA GOOOO!” he yelled.
Which was a good point, really, because it would not have behooved me to have stopped mid-race. So go I did.
Anyway, he often yelled my splits at me as I passed.
“1:45, DJ!” he yelled.
OK, said my 16-year-old brain. So multiply that by 7.5 laps, and…dear God, I have to speed up and also find another sport, because I’m going to cross that finish line and vom. And for what? A middle-of-the-pack finish, that’s- THAT STUPID BITCH JUST FLAT-TIRED ME I’M GONNA WAAAAAIL ON HER.
“GOOOOOOOO!” added Coach.
You magnificent rhetorical genius, said my brain.
But the tendency to work out complicated math problems also carried over to my training runs. Back when a 6-mile run was a big deal for me, it was a time to clear my head and think on the quiet country roads, and ponder derivatives and slopes and asymptotes and limits and wonder whether, if I ran a little more or aced a few more calc tests as a result of my running more, Tommy Van Der Hagen might finally want to date me, or at least tell his girlfriend to stop calling me “Vag-face” in an unnecessarily loud voice in front of authority figures in the halls, forcing me to body-check her in basketball practice later that day, and then every day for the rest of the season.
“Vag-face, we’re STRETCHING. The scrimmage hasn’t even STARTED yet,” she would say.
“<forceful-headbutt-to-the-sternum>,” I would respond.
“BITCH!” she would yell.
“I KNOW CALCULUS!!!” I would howl victoriously, giving her a sports-bra-wedgie.*
Anyway. I still like to do math problems in my head while I run, because–not unlike podcasts–it gives me something to think about during long runs other than the steady growing ache in my hip tendons. Below is a sampling of math-AND-running-related problems for you to work out on your next jog.
Work quickly, show your work, grades will be passed out tomorrow.
1) A female runner was jogging along the C & O trail last Saturday, minding her own business, when she struck her clumsy foot upon a rock, sending her tumbling to the ground and scraping skin off of all of her right-side appendages in the process.
(a) Given that the runner is 140 pounds and was traveling at roughly 7 miles per hour, how far did she skid/bounce before coming to a halt at the feet of a kindly-looking running couple?
(b) Given the above weight and velocity, as well as the fact that the wind was from the east at 8 miles per hour, how many times did the woman who picked the runner back up unnecessarily say, “Oh, bless your heart!”?
(c) How many miles can said runner continue without looking at the blood dripping out of her palm and getting all woozy and shaky-legs?
2) A runner is jogging away from her home, which is along a diagonal street, represented by C in the diagram below, a street which is intersected by perpendicular streets A and B. Said runner wants to get to the other end of side C, where untold running happiness (i.e., Rock Creek Park on the weekends) awaits. Only problem is the innumerable Pervy Perverson dudes hanging out outside of the innumerable liquor stores along street C, who yell dirty things (“I wanna HIT THAT!”) and nonsensical things (“Where the PARTY AT, girl?”) and James-Brown-lyric-sounding things (“Hit it and quit!”). Said runner does not tolerate drunken harassment from anyone, aside from her housemates, as well as delightfully impressionable young Hill intern dudes, in town just for the summer and out at the bars all night in their brand-spanking-new suits, just hoping to make a friend or two, that’s all, when lo and behold in swoops an older, awkward but charming blonde journalist sort, cooing in a reassuring voice such gems as, “Oh baby listen, was Senator McConnell mean to you? Aw, that’s too bad. Have another gimlet or five and walk me home and gimme the DL.” Awwwww girl.
(a) Assuming the runner wants to avoid street C, and assuming that angle CA is 65 degrees and street C is 4 miles long, how much longer will the new path along streets A and B be?
(b) Using the formula
M = (i^2 + H)/A
…where M is “miles a runner is willing to go out of her way,” i is “how irritated is she on a scale of 1 to 10?” and H is “hotness quotient as determined by the good folks on Hotornot.com,” and A is Avogadro’s Number, is this detour going to be worth it?
(c) Said runner is trotting along, when suddenly across a park she sees one of the Pervy Perversons, only to spot, with her finely tuned eyes, a HILL ID BADGE holy God it’s an intern SWARM SWARM!
…so how long will the new route, from angle AB to point 1, take her to run, assuming that she increases her speed from 7 to 12 mph and leaps over a few park benches in the process?
3) Assuming a runner goes through seven gels a weekend, at $1.29 a pop, plus finally buckled a few weeks ago and bought a $50.99 fuel belt (plus whatever the DC sales tax is) and furthermore runs 85 miles a week, buying a new pair (costing roughly $90, again with sales tax) every 500 miles, and also showering twice a day and washing lots of clothes because of her truly remarkably awful running-funk and upping the water bill by $10 each month, how much…no, wait…better question: how hard is she going to have to work to NOT realize that she could be just as happy by spending all that money on a bottle of Jim Beam and a Netflix queue fullllllllll of shirtless-Matt-Damon movies?
4) A 110-pound, 42-year-old female runner has eaten 1200 calories today, most of it in the form of seaweed and wheat germ, and has run 35 miles today, at 6.8 mph, burning 600 calories per hour, and has also drunk 2 gallons of green tea to kick off her weekend master cleanse. Assuming that burning 3500 calories equals shedding one pound and that her body fat composition is 14 percent, will you please punch me in the face if I ever become this person?
5) Let f(x) = (x^2 + 1)/(x+2).
(a) Using L’Hopital’s Rule, what is the limit of f(x) as x approaches 3?
(b) I STILL KNOW CALCULUS! <gives you a sports-bra wedgie>
EXTRA CREDIT: Is Tommy Van Der Hagen still single?
*Don’t know what it is? Come over here and I’ll show you.