Question

A tourist purchases a car in England and ships it home to the United States. The car stickers advertised that the car's fuel consumption was the rate of $$40$$ miles per gallon on the open road.
The tourist does not realize that the $$U.K.$$ gallon differs from the $$U.S.$$ gallon:
$$1\ U.K.$$ gallon $$=4.546\ 090\ 0$$ litres
$$1\ U.S.$$ gallon $$=3.785\ 411.8$$ litres
For a trip of $$750$$ miles (in the United states), how many gallons of fuel does
the mistaken tourist believe she needs

Answer 1

This problem compares the $$U.K$$ gallon with $$U.S.$$ gallon two non $$SI$$ units for volume. The interpretation of the type of gallon whether $$U.K$$ or $$U.S.$$ affects the amount of gasoline one calculate for travelling a given distance.
If the fuel consumption rate is $$R$$ (in miles/gallon), then the amount of gasoline (in gallons) needed for a trip of distance $$d$$ (in miles) would be
$$V$$ (gallon)$$=\dfrac{d(miles)}{R(miles/gallon)}$$
Since the car was manufactured in the $$U.K.$$ the fuel consumption rate is calibrated based on $$U.K.$$ gallon and the correct interpretation should be $$40$$ miles per $$U.K.$$ gallon. In $$U.K.$$ one would think of gallon; however in the $$U.S.$$ the word gallon would naturally be interpreted as $$U.S>$$ gallon. Note also that since $$1\ U.K.$$ gallon $$=4.5460900\ L$$ nad $$1\ U.S.$$ gallon $$=3.7854118\ L$$, the relationship between the two is
$$1\ U.K.$$ gallon $$=(4.5460900\ L)\left(\dfrac{1.\ U.S\ gallon}{3.7854118\ L}\right)=1.20095\ U.S$$ gallons
The amount of gasoline actually required is
$$V'=\dfrac{750\ miles}{40\ miles/U.K\ gallon}=18.75\ U.K$$ gallons $$\approx 18.8\ U.K.$$ gallons
This means that the driver mistakenly believe that the car should need $$18.8\ U.S$$ gallons