Mental Exercise: How fast did I go?

[Zilch]

Ok, this might keep some of you occupied for a bit, and I am going nuts trying to figure this out.

The story is this: I am recovering from stress fractures while trying to stay in shape and improve my overall fitness. My physical therapist has me doing a 3/1 walk/run. This means I am walking briskly for three minutes and then running for one minute.

It so happens that I covered almost exactly 1 mile during a 12 minute walk/run event. I'm trying to extrapolate how fast I was going during the running portion. (This way I could know how fast I would have covered my three miles for a PFT, given that I maintain that speed once my bones are up to it.)


Initially, I figured I had run for 1/4 of the time, so I must have covered 1/4 of that mile. But, NO! I was running faster for that time, so I covered more distance. Catchy, eh?

So, I'm stumped on it, and my nerdy friends here are working on it but have no solution yet. Any takers? I figure some of you more navigationally-trained professionals might have some fancy formulas that I don't.

Oh, the obvious solution of having me run a set distance and timing it...well, that would make too much sense.

I give rep to the first one to answer, if it's mathematically possible.

 

[Kickflip89]

you've got two unknowns: The basic equation would be

9w + 3r = 1,

where w and r are the walking and running speeds in units of miles/minute. So, time yourself walking a mile at the same pace, use that as your w and solve for r:

r = 1/3*(1-9w).

Then, use that to figure out the 3 mile time if you could sustain that pace for 3 miles. i.e. t = 3/r.

Example, let's say you walked at 3.5 mph, or about .0583 mpm, that means your "r" is about .1583 or 9.5 mph, which gives a 3 mile time of about 19 minutes.

In this example you would have ended up running just about 1/2 a mile, which is obviously a lot different than running 3 miles, so the mathematical estimate might not be a great indicator.

 

[Intruder Driver]

Google Jeff Galloway. I used his training method, which is a walk/run one, to train for and run two marathons in 30 days. I no longer have his training manual, but it covers this.

 

[MasterBates]

NERDS!!

 

[Zilch]

Groovy...I'll be pretty happy if I can keep that pace up all the way through three miles.

"On the Moon, nerds have their pants pulled down and they are spanked with moon rocks!"

 

[muc1]

here's a quickie calc if you know your walking pace...

Pace = 60/[20-3(walking speed)]
fewer conversions

if your walking speed is 3.5, then
60/20-3*3.5 = 6.13 minutes/mile (same as above)

 

[DimndDave14]

If you want to get a little more in depth you could measure out the distance you ran. Because the 3.5 mph for walking variable is the average fast pace walk for a man. This does not include if you are pushing yourself, hilly terrain or stride length. Also the 19 minute estimate run does not show fatigue that you would get with a consistent three miles. But that does not mean you should not shoot for 19 minutes or even better when you’re at 100%


PS Ogre also turned into a NERD as well

 

[jfulginiti]

You're going about it all wrong man...... you need to get really REALLY drunk first......

 

[Slammer2]

bingo...then do the crunches afterwards...you get drunk all over again

 

[Zilch]

Good call! I'll do that for today's PT...got lots of Guiness hiding in the fridge.

 

[KC130FE]

NERDS!!

Concur!

 

[Pitchlock]

you've got two unknowns: The basic equation would be

9w + 3r = 1,

where w and r are the walking and running speeds in units of miles/minute. So, time yourself walking a mile at the same pace, use that as your w and solve for r:

r = 1/3*(1-9w).

Then, use that to figure out the 3 mile time if you could sustain that pace for 3 miles. i.e. t = 3/r.

Example, let's say you walked at 3.5 mph, or about .0583 mpm, that means your "r" is about .1583 or 9.5 mph, which gives a 3 mile time of about 19 minutes.

In this example you would have ended up running just about 1/2 a mile, which is obviously a lot different than running 3 miles, so the mathematical estimate might not be a great indicator.

Nice try, but you need to account for acceleration and deceleration between walking and running transitions....I'll leave it a an exercise....ha, ha. (in my best nerd voice)