A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption was at the rate of 39 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon, as shown below. 1 U.K. gallon = 4.546 090 0 liters 1 U.S. gallon = 3.785 411 8 liters.
(a) For a trip of 650 miles (in the United States), how many gallons of fuel does the mistaken tourist believe she needs? gal
(b) How many gallons does the car actually require? gal
It looks like an impossible problem, since there's no way to convert L to miles...
I have 39 miles / 1 UK gal * 4.5460900 UK gal / 1 L, but I can't go any further because there's nowhere to put 650 miles.
There are only a few quantities floating around this problem (for part a, say):
$1)$ $ \frac{ 39 miles}{U.K. gallon}$ $2)$ $ \frac{4.5 liter}{U.K. gallon}$ $3)$ $ \frac{3.8liter}{U.S. gallon}$
What we want to know for part a) is what the tourist believes her gas mileage is, i.e. what her gas mileage is in U.K. gallons. This is given. For part b), we want to know her gas mileage in U.S. gallons. So, using only multiplication and inversion of fractions, how can the above quantities be arranged to find $\frac{\_\_\_U.S. gallons}{mile}$? Figure this out, and then multiply by the number of miles she is traveling.