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Author Topic: My math is bad  (Read 14406 times)

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GTRS Fiero

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My math is bad
« on: April 07, 2018, 12:19:13 pm »
I hadn't ever really thought about it previously, but I wanted to know how fast I ran, so I ran the numbers...and made a mistake somewhere.

400 meters in 48 seconds = 8 1/3 meters per second
1 mile = 5280 feet, or 1320 meters
By extension, my time would have been 1 mile in 158.4 seconds or 2.64 minutes or .044 hours
To find my average speed for 400 meters in MPH, I used a ratio:
1 mile is to .044 hours as x miles is to 1 hour
OR
x MPH = 1 mile * 1 hour / .044 hours
x = 22.72727 MPH

I worked this a different way:
1 mile / (2.64 minutes per mile / 60 minutes per hour) = 22.72727 MPH
Same answer.

I re-checked my math:
conversion from 400 meters to 1 meter (48 seconds / 400 meters) = .12 seconds per meter
1320 meters per mile * .12 seconds per meter = 158.4 seconds per mile
OR
48 seconds / 400 meters = x seconds / 1320 meters per mile
x = 158.4
OR
1320 meters per mile / 8 1/3 meters per second = 158.4 seconds per mile

That seemed highly unlikely, given that I had been told that a human could only run about 23 MPH.  There are faster sprinters than I was, which is why I had to run in circles, instead of the more worthwhile 100m dash where at least the runner got from point A to point B.

Had anyone asked, I'd have guessed that my average speed was around 15MPH for 400 meters.  I knew that I could run 200 meters in the 22s.  With this math, that's about 24 MPH.  I ran the 100 meter-dash in about 10.8 seconds, which this math shows as about 25.25 MPH.  That wasn't fast enough to be competitive, so I was put in the 400-meter events.  I had been told that that was a quarter mile, and never thought about it, but the math shows that 1 mile (1320 meters) divided by 4 = 330 meters (a quarter mile), which means that the 1600 meter relay was 1.21 miles.  I remember running heat races, where the second-place team in our heat was still entering the final turn when I crossed the finish line, and we weren't the winning team.

So, I looked up the top speed for a human, and it's 28MPH.  Probably at a certain temperature and altitude, with the wind either still or at the person's back.  Anyway, something seems to be wrong with my math.  My times and distances are correct, because the distances were measured by regulation, and they used electronic timing.

The track coach always told me I was slacking.  I'm not sure if these numbers support his view or mine.  When I was 11 or so, I used to compete against people from all over, and generally won, except against a particular guy who was about 5 years older than I was.  They clocked me at 22MPH, 90 degrees F, at 318 feet, high humidity and partly sunny, so I figured that was my top speed.  In a 3-day competition in Denver, I never hit 22 MPH.  My worst times were in California, but I blamed that on lack of sleep and the bad air.

GTRS Fiero

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Re: My math is bad
« Reply #1 on: April 07, 2018, 12:38:02 pm »
My dad has always held that he ran the quarter mile faster than I did, but his quarter mile was 440 feet.  I ran the numbers.  On the face of it, 4 feet per meter, or 3 feet per yard, 440 yards sounds good.  My dad would always divide 440 yards by 3 feet and get 146 2/3, compared to 400 divided by 4 which is only 100.  When he multiplied by 4, it made me look like a slowpoke.
 Compounded by his 2-second lower time, it would seem that his numbers are better, but it's feet per yard, not yards in a foot, so it should be multiplied.  That's 1600 feet I ran, and only 1320 feet he ran, which means I ran 280 feet further than he did.

By this math, he only averaged 19.56 MPH in the quarter, but he was a 200-meter runner.  We never compared times in the 200-meter dash, because I never got to compete at a state level.  No matter, he still has more wins than I had.

ron768

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Re: My math is bad
« Reply #2 on: April 07, 2018, 01:03:16 pm »
Never ran til I joined the Army. My best 2 mile time was 12 minutes 6 seconds. I did train with a guy who could run 2 miles in 9 minutes and 30 seconds.
1985 2M6 SE, 1986 GT x 2.

GTRS Fiero

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Re: My math is bad
« Reply #3 on: April 07, 2018, 02:17:14 pm »
I'm not a distance runner.  Were you in full gear, boots, and carrying both your rifle and your pack for that run?  My gear, rifle, and pack weighed only about 100 pounds, but the guys in uniform carried 20 pounds more, and those boots aren't made for speed or comfort.

I ran 7 miles in 26 minutes, with incentive (16.15 MPH), but in competition, ran 5K in 28 minutes (6.69 MPH).  I was going to do a 40-mile hike as part of a decathlon, this month, but missed the deadline for signing up.  My wife says I'm too old for that, anyway, but I'm almost too old to enter.

I don't know what a good 2-mile time is, because we were running 3200 meters as 2 miles; however, I can figure your speed.  You ran 2640 meters in 726 seconds.  That's 9.91 MPH.  Your friend averaged 12.63 MPH.

My math may be in greater error here.  I just multiplied the meters for 1 mile by however many miles.

You probably could have run faster before boot camp.  The Army took the speed out of everyone I knew.  While you're running, it feels as if you're putting a lot of effort into it, but later the numbers don't look so good.  Coaches show you segment times where maybe segment 2 or 3 was 2 seconds faster than the previous segment, which means that you weren't trying your best.  I am not good at running against the clock--particularly when I'm not having fun.  The coach would show that other runners has almost identical segment times.  In AAA my junior year, I ran legs 1 and 4 of the 4x400 at one meet, because one of our runners was injured. Everyone agreed beforehand that this would be OK, and the alternative for us was to forfeit.  I collapsed after the race, but the coach was pissed at me, because my time on leg 4 was faster not only than my time on leg 1 but also than my 400-meter dash time.  We won the event, so I didn't see what the problem was.  The unjured runner got credit for my time, but the second place team tried to have our effort disqualified.  I know now that I should've been treated after my collapse, but the coach just left me to suffer, at the time.  If anyone else has this happen to them, someone should ensure you walk until cool-off, clear your breathing to prevent adema (sp), get a towel to keep you from catching cold, stretch, and get liquids.

It took me a week to recover.  I don't know what my time was for leg 4, and it isn't published like times are now.  My comment was that I was in front on leg 1, and behind on leg 4, because someone did a poor job of handing off the baton.  The coach said I was sandbagging.

By my senior year, my knees were destroyed, but I probably wouldn't have run in college, anyway.  They used trickery to make me run in HS, and I no longer enjoyed it.  I felt abused and taken advantage of.  Running now is painful.  I don't have the strength or muscle mass I had then.  Also, the speed just isn't there.  I get to a certain point, and it's as if I hit a wall.  I know I used to run faster.  I used to enjoy running, too.  It was exhilarating.

pgackerman

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Re: My math is bad
« Reply #4 on: April 07, 2018, 04:21:05 pm »

Looked here: https://www.google.com/search?q=meters+per+second+to+miles+per+hour&oq=meters+per+&aqs=chrome.0.0j69i57j0l4.6118j0j8&sourceid=chrome&ie=UTF-8

Came up with 18.64 MPH.

400meters/48sec * 1 miles/1609.34meters* 3600sec/hour =18.64118196 MPH


Now given:
X = Y
X**2 = XY == Y**2      BTW, X**2 is X * X or X squared or X2

X2 - Y2 = XY - Y2   Adding/Subtracting the same amount by both sides
(X-Y)(X+Y) = Y(X-Y)            Factoring.  All perfectly legal
(X+Y) = Y                           Divided by X-Y
X + X = X                           Cuz X = Y
2X = X                               Um, addition
2 = 1                                 Divided by X

So there!

Red '88 GT 5-Speed, 7730ECM, 1.6 Rockers, and KEYLESS Entry! 
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ron768

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Re: My math is bad
« Reply #5 on: April 07, 2018, 04:39:13 pm »
In boots and gear , I ran much slower. This time was for a PT test. From 32 yo to 38 yo, I ran 2 miles in this time or a few seconds more. My distance run was 20 klicks in 3 hours with boots and gear in uniform.
1985 2M6 SE, 1986 GT x 2.

GTRS Fiero

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Re: My math is bad
« Reply #6 on: April 07, 2018, 05:23:43 pm »
Hmmm.  That shows my dad averaging 19 MPH.  So, where is my math error?

18 MPH is much more reasonable.
« Last Edit: April 07, 2018, 05:46:49 pm by GTRS Fiero »

GTRS Fiero

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Re: My math is bad
« Reply #7 on: April 07, 2018, 05:46:25 pm »
Now given:
X = Y
X**2 = XY == Y**2      BTW, X**2 is X * X or X squared or X2

X2 - Y2 = XY - Y2   Adding/Subtracting the same amount by both sides
(X-Y)(X+Y) = Y(X-Y)            Factoring.  All perfectly legal
(X+Y) = Y                           Divided by X-Y
X + X = X                           Cuz X = Y
2X = X                               Um, addition
2 = 1                                 Divided by X

So there!

No.  (X-Y) = 0, since X=Y
You cannot divide by zero.  Before that, you have zero = 0.

Of course, Pluto used to be a planet, so maybe math changed.

pgackerman

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Re: My math is bad
« Reply #8 on: April 07, 2018, 06:01:04 pm »

Right you are!

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GTRS Fiero

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Re: My math is bad
« Reply #9 on: April 07, 2018, 06:20:11 pm »
We used to set up our calculus, trig, and geometry teachers with all sorts of these in high school. The intersecting parallel lines was a favorite.  I recall a really neat problem we had for the calculus teacher.

GTRS Fiero

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Re: My math is bad
« Reply #10 on: April 09, 2018, 07:51:07 pm »
Hmmm.    I was using 4 feet to a meter, rather than 3.28.  Found my error.