Average pace, vs, average speed, harmonic mean example - Videos


Average pace, vs, average speed, harmonic mean example,

This is my hardest math video to make so far. You can also see the solutions @1:50 ,

harmonic mean, San Francisco Marathon 2017, running vlog,

average of 6 mph and 4 mph is NOT 5 mph,
Filmed on GoPro4 session, & iPhone6,
classic tricky question,
math for fun,
average speed,
average pace,
how to find the harmonic mean,
San Francisco Marathon 2017,
Run & Math,
harmonic average,
google parker pen,




  1. Intuitively speaking assuming it's a step function which goes from 6 to 4, you will spend more time in 4 building up the area beneath the curve AKA the distance traveled. As such a perfect way to model this is weighing the smaller number which is why the reciprocal is useful beyond simply giving the correct units it's derivative is descending 1/4<1/6. Of course this all just coincides with the fact the units match up and the formulas match up

  2. Why do you do both mathematics and athletic/sports stuff in your life instead of just one xor the other? Is it required to do both instead of just one xor the other? Is one a bad person if you only do one xor the other and not both? This is a rather odd obsessional topic of mine and I want to hear opinions of various sorts about this due to the strange tension in my head and gut that it seems to bring up.

  3. Video is tau minutes long

    Note: for all the ppl that are gonna go like ''thats not actually tau minutes long in hexadecimal its actually blah blah'' just let people enjoy things

  4. small error: lowest common denominator of 12 and 8 is 24, not 48. The mistake doesn't effect your answer, but calling 48 the lowest common denominator might confuse some people.

  5. Let's say that a marathon is x miles.

    for the first x/2 miles you travel at 10 min/mile (faster)

    for the second x/2 miles you travel at 12 min/mile (slower)

    For the sake of simplicity, let x =2. So for the first mile it takes 10 minutes and for the second mile it takes 12 minutes. So your average speed would be ( 1/10 ) miles/ minutes * (10/22) + ( 1/12 ) miles/minute * (12/22) = 2/22 miles/minute

    So that means the average pace would be 22/2 minutes/ mile

  6. 1. Great job running a 4:41:00 marathon while talking and holding a go pro stick at the same time!
    2. LCD in your avg speed calculation should be 24, not 48, no big deal 🙂
    3. Aren't we runners genius for coming up with an invariant for measuring our pace…it withstands the nasty harmonic mean calculation!
    3.5 My PR = 3:40:00 at '15 NYC marathon 🙂

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  8. d = s * t == > d / s = t

    total distance = d1 + d2

    average rate = ( d1 + d2 ) / [ (d1 / s1) + (d2 / s2) ]

    average rate = (d1 + d2 ) * s1 * s2 / [ d1*s2 + d2 * s1 ]

    average rate = s1 * s2 / [ ( d1 / (d1 + d2 ) )*s2 + ( d2 / ( d1 + d2 ) )*s1 ]

    Now if d1 = d2 we get :

    average rate = s1 * s2 / [ ( 1 / 2 )* s2 + ( 1 / 2 ) * s1 ]

    average rate = 2 * s1 * s2 / ( s1 + s2 ) This is called the harmonic mean.


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