Question 0.7: Complex Unit Conversions A large sport utility vehicle movin......
Complex Unit Conversions
A large sport utility vehicle moving at a speed of 125 km/h might use gasoline at a rate of 16 L per 100 km. What does this correspond to in mi/gal?
STRATEGY
We are given a gasoline mileage in the units L/km (or km/L), and we need to find the mileage in the units mi/gal. Thus, two conversions are necessary, one from kilometers to miles and one from liters to gallons. It’s best to do multiple conversions one step at a time until you get used to them. First, convert the distance from kilometers to miles and the amount of fuel from liters to gallons, and then divide the distance by the amount of fuel to find the mileage.
\frac{62.14 \mathrm{mi}}{4.22 \mathrm{gal}}=14.73 \frac{\mathrm{mi}}{\mathrm{gal}} Round off to 15 mi/gal
Notice that extra digits are carried through the intermediate calculations and only the final answer is rounded off.
When you become more confident in working multiple conversion problems, you can set up one large equation in which all unwanted units cancel.
\frac{100 \ \cancel{km}}{16 \ \cancel{L}} \times \frac{3.79 \ \cancel{L}}{1 \ \mathrm{gal}} \times \frac{0.6214 \ \mathrm{mi}}{1 \ \cancel{km}}=14.73 \frac{\mathrm{mi}}{\mathrm{gal}} Round off to 15 mi/gal
BALLPARK CHECK
The mileage is probably low, perhaps around 15 mi/gal. This is a difficult problem to estimate, however, because it requires several different conversions. It’s therefore best to think the problem through one step at a time, writing down the intermediate estimates:
• A distance of 100 km per 16 L is approximately 6 km/L.
• Because 1 km is about 0.6 mi, 6 km/L is about 4 mi/L.
• Because 1 L is approximately 1 qt, or 1/4 gal, 4 mi/L is about 16 mi/gal.
Tis estimate agrees with the detailed solution.