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Math Help - Rather basic conversion formula.

  1. #1
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    Rather basic conversion formula.

    Hey all. Good to be here. Do need some random conversion help, shouldn't be particularly difficult.

    Basically I want to convert litres per 100km into miles per imperial gallon

    The basic conversions are:
    1 mile = 1.6km
    1 imperial gallon = 4.55L

    1km = 0.62mi
    1L = 0.22 imperial gallon.

    All I want really is a formula that can convert xL/100km into ympg

    I would like to know how to justify a formula starting with just the above values. I do know what the final formula is, but the L/100km being a fraction kind of throws my understanding of how the formula would work.

    Thanks a lot
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  2. #2
    MHF Contributor
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    Hello dredgy

    Welcome to Math Help Forum!
    Quote Originally Posted by dredgy View Post
    Hey all. Good to be here. Do need some random conversion help, shouldn't be particularly difficult.

    Basically I want to convert litres per 100km into miles per imperial gallon

    The basic conversions are:
    1 mile = 1.6km
    1 imperial gallon = 4.55L

    1km = 0.62mi
    1L = 0.22 imperial gallon.

    All I want really is a formula that can convert xL/100km into ympg

    I would like to know how to justify a formula starting with just the above values. I do know what the final formula is, but the L/100km being a fraction kind of throws my understanding of how the formula would work.

    Thanks a lot
    If we use x L to cover 100 km, that's x L to cover 100\div 1.6 = 62.5 miles

    So how many gallons are there in x L? Answer x \times 0.22=0.22x.

    So we've covered 62.5 miles using 0.22x gallons, which is 62.5\div 0.22 x miles per gallon.

    So there's our formula:

    y=62.5\div 0.22 x

    = \frac{62.5}{0.22 x}

    \approx \frac{284}{x}

    So, for example, 8 L per 100 km \approx \frac{284}{8}=35.5 mpg

    Grandad
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