Can I get some help please

Question

You decide to take your car on a drive through, where gas is sold in liters and distances are measured in kilometers. Suppose your car's gas efficiency is 36.0 mi/gal. How many liters of gas will you need to complete a 482 km trip? Use the conversions 1 gal = 3.78 L and 1 km = 0.6214 mi.

Answer 1

So Janet J.,

You are going to use "dimensional analysis" again.

Start with your given "hard datum" : 482 km. You need to eventually get to L, right? So what's related to L? Gal, right? And what's related to Gal? mi, right? And what's related to mi? km, right? So now, do that path in the reverse of what is listed there:

km -> mi -> Gal -> L

and here's how you do it:

482 km * (0.6214 mi/km) / (36.0 mi/Gal) * (3.78 L/ Gal) .

Do you see how you progressively change the units, until you end up with exactly what you need, in the proper place (numerator vs. denominator)? Essentially, you have multiplied (or divided) by several Conversion Factors, which are just ways of writing the value "1" (which you can always multiply or divide by, no problem!), except that they (Conversion Factors) have numeric values AND pairs of units, such that they DO represent "1": 1 Gal = 3.78 L (exactly, for this problem), so multiplying by (1 Gal/3.78 L) is just like multiplying by "1". And so on. Does that make the process a bit clearer?

-- Cheers, --Mr. d.