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Fuel consumption is a measure of how efficiently a vehicle uses fuel to travel a certain distance. In simple terms, it tells us how many miles a car can drive per gallon of gasoline. For example, if a car has a fuel consumption rate of \(20 \text{ mi/gal}\), it means the car can travel 20 miles on one gallon of gas. Understanding fuel consumption is important for both economic and environmental reasons.

• **Economic Impact**: Better fuel efficiency means spending less money on gas.
• **Environmental Benefit**: Lower fuel consumption reduces carbon emissions, helping to protect the environment.

Improving fuel efficiency involves using less gas to go the same distance. In this exercise, increasing the fuel consumption rate from \(20 \text{ mi/gal}\) to \(25 \text{ mi/gal}\) drastically saves fuel, which we will elaborate on in the next sections.

The concept of gallons per mile helps us understand fuel consumption from a different perspective. Typically, we see fuel efficiency expressed in miles per gallon (mpg), but flipping it gives us gallons per mile.

• This tells us how much gas is needed to travel a single mile.
• Lower gallons per mile indicate better fuel efficiency.

For instance, if a car uses \(\frac{1}{20}\) gallons to travel a mile, it is less efficient compared to using \(\frac{1}{25}\) gallons per mile. To calculate gallons per mile, you simply take the reciprocal of miles per gallon:\[\text{Gallons per Mile} = \frac{1}{\text{Miles per Gallon}}\]By using this measure, it is easier to calculate how a change in fuel consumption rate impacts the total fuel used over a set distance. In our example, moving from \(\frac{1}{20}\) gallons per mile to \(\frac{1}{25}\) gallons per mile is more efficient and results in significant fuel savings.

Distance traveled refers to the total number of miles covered by a vehicle over a period, typically a year. In this exercise, each car travels an average of \(10,000 \text{ miles/year}\). Distance traveled is critical in calculating overall fuel consumption because it multiplies the rate at which fuel is consumed per mile.

• To compute total fuel used: multiply distance by gallons per mile.
• The longer the distance, the more important fuel efficiency becomes.

For example, at a fuel consumption rate of \(20 \text{ mi/gal}\), a car traveling \(10,000 \text{ miles}\) will use 500 gallons of gas:
\[\text{Fuel Used} = \frac{10,000 \text{ miles}}{20 \text{ mi/gal}} = 500 \text{ gallons}\]If the fuel consumption rate improves to \(25 \text{ mi/gal}\), only 400 gallons are needed for the same distance, indicating 100 gallons saved per car. Thus, altering the fuel efficiency of millions of cars can save a gigantic total amount of gasoline, demonstrating how crucial fuel consumption optimization is.