# Rather basic conversion formula.

• Oct 27th 2009, 05:19 AM
dredgy
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 :)
• Oct 27th 2009, 06:26 AM
Hello dredgy

Welcome to Math Help Forum!
Quote:

Originally Posted by dredgy
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 $\displaystyle x$ L to cover $\displaystyle 100$ km, that's $\displaystyle x$ L to cover $\displaystyle 100\div 1.6 = 62.5$ miles

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

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

So there's our formula:

$\displaystyle y=62.5\div 0.22 x$

$\displaystyle = \frac{62.5}{0.22 x}$

$\displaystyle \approx \frac{284}{x}$

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