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Anybody good at math?

Discussion in 'Gen 3 Prius Fuel Economy' started by kalome, Nov 1, 2012.

  1. kalome

    kalome Member

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    Can someone please help me get the average miles per gallon for my work round-trip including lunch round-trip?

    I take the freeway to work which is 16.7 miles. Lunch round-trip 3 to 5 miles. Take surface streets home from work 12.5 miles.
    Going to work I get anywhere from 56 to 60 miles per gallon, dash reading. Lunch round-trip depending on where I go could be as low as 50 miles per gallon. Going home from work anywhere from 82 to 88 miles per gallon.

    So a low estimate average:

    58 mpg for 16.7 miles
    84 mpg for 12.5 miles
    50 mpg for 3 miles

    58 - 51.86% of the 3 routes
    84 - 38.82% of the 3 routes
    50 - 9.31% of the 3 routes

    What would be the average miles per gallon for all 3 routes?
     
    #1 kalome, Nov 1, 2012
  2. markabele

    markabele owner of PiP, then Leaf, then Model 3

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    64.8
     
    #2 markabele, Nov 1, 2012
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  3. kalome

    kalome Member

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    Could you show me how you arrived to that average?
    A straight average without using distance would be 64.
     
    #3 kalome, Nov 1, 2012
  4. schlem

    schlem Polygeek

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    I would set a trip computer for the day and let the ODO average all the mileage, but I think the math is relatively simple.

    58 MPG X 16.7 Mi = 968.6 Mi^2PG (to coin a unit: "Miles squared per gallon")
    84 MPG X 12.5 Mi = 1050 Mi^2PG
    50 MPG X 3 Mi = 150 Mi^2PG
    Total = 2168 Mi^2PG

    2168 Mi^2PG divided by 32.2 total Mi traveled = 67.35 MPG (notice that Miles cancel and the correct unit MPG is returned.)
    Pretty Freakin Awesome, what?
    Someone check my math?
     
    #4 schlem, Nov 1, 2012
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  5. kalome

    kalome Member

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    Cool! Thank you.
    67.33 MPG rounded, right?
     
    #5 kalome, Nov 1, 2012
  6. ken1784

    ken1784 SuperMID designer

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    Column 1
    0 [tr][th]route[/th][th]mpg[/th][th]miles[/th][th]gallons[/th][th]mpg total[/th][/tr]
    1 [tr][td]1[/td][td]58[/td][td]16.7[/td][td]0.29[/td][td]-[/td][/tr]
    2 [tr][td]2[/td][td]84[/td][td]12.5[/td][td]0.15[/td][td]-[/td][/tr]
    3 [tr][td]3[/td][td]50[/td][td]3.0[/td][td]0.06[/td][td]-[/td][/tr]
    4 [tr][td]total[/td][td]-[/td][td]32.2[/td][td]0.50[/td][td]64.8[/td][/tr]


    Ken@Japan
     
    #6 ken1784, Nov 2, 2012
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  7. schlem

    schlem Polygeek

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    [edit] seems I screwed it up [\edit]
     
    #7 schlem, Nov 2, 2012
  8. kalome

    kalome Member

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    Ah....so markabele was right. :)

    Thanks Ken.
     
    #8 kalome, Nov 2, 2012
  9. schlem

    schlem Polygeek

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    Quoting-an-embedded-matrix-issues aside...

    Ok, I understand this methodology, but why does my math differ?
     
    #9 schlem, Nov 2, 2012
  10. ken1784

    ken1784 SuperMID designer

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    Let's take another example...
    route-1 50 mpg for 100 miles
    route-2 100 mpg for 100 miles

    your math
    Column 1
    0 [tr][th]route[/th][th]mpg[/th][th]miles[/th][th]m^2pg[/th][th]mpg total[/th][/tr]
    1 [tr][td]1[/td][td]50[/td][td]100[/td][td]5000[/td][td]-[/td][/tr]
    2 [tr][td]2[/td][td]100[/td][td]100[/td][td]10000[/td][td]-[/td][/tr]
    3 [tr][td]total[/td][td]-[/td][td]200[/td][td]15000[/td][td]75[/td][/tr]


    my math
    Column 1
    0 [tr][th]route[/th][th]mpg[/th][th]miles[/th][th]gallons[/th][th]mpg total[/th][/tr]
    1 [tr][td]1[/td][td]50[/td][td]100[/td][td]2[/td][td]-[/td][/tr]
    2 [tr][td]2[/td][td]100[/td][td]100[/td][td]1[/td][td]-[/td][/tr]
    3 [tr][td]total[/td][td]-[/td][td]200[/td][td]3[/td][td]66.7[/td][/tr]


    I believe my math is correct.

    Ken@Japan
     
    #10 ken1784, Nov 2, 2012
  11. Adam Leibovitch

    Adam Leibovitch Member

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    Edit: Oh nevermind, just see what Ken said
     
    #11 Adam Leibovitch, Nov 2, 2012
  12. schlem

    schlem Polygeek

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    Your math is the better, elegant, and obvious solution. I'll take my head-scratching offline for now.

    I sit at your feet.
     
    #12 schlem, Nov 2, 2012
  13. Adam Leibovitch

    Adam Leibovitch Member

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    Is it like saying that since you drive to work at 20mph and drive home at 30mph, you average 25 mph for the trip, but thats not right because you used more time to get to work at 20mph, so your average speed is lower than 50/50? Just like OP uses more gallons at a lower mpg's?
     
    #13 Adam Leibovitch, Nov 2, 2012
  14. Codyroo

    Codyroo Senior Member

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    The simple answer is that you can't average averages to get the correct average. (you will not get the correct answer if you average 2 means).
     
    #14 Codyroo, Nov 2, 2012
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