The Honda Civic Hybrid vehicle, powered by gasoline-electric...

The Honda Civic Hybrid vehicle, powered by gasoline-electric technology, gets 49 miles per gallon (mpg) in city driving and 51 mpg in highway driving (Source: Honda.com). The car is driven $447 \mathrm{mi}$ on 9 gal of gasoline. How many miles were driven in the city and how many were driven on the highway?

Key Concepts

System of Linear Equations

In many problems where there are two or more unknowns, setting up a system of linear equations is a key strategy. This involves writing different equations based on the conditions provided (such as total distance and total fuel consumption) and then solving them simultaneously using methods like substitution or elimination to find the values of the unknowns.

Rates and Ratios

Rates, such as miles per gallon (mpg), express the relationship between two different quantities—in this case, distance and fuel. Understanding ratios is crucial because they allow you to determine how variations in consumption rates (different mpg for city and highway driving) affect the overall outcomes, enabling the formulation of equations based on these unit measures.

Weighted Averages

When an overall average is influenced by quantities that vary in size or importance, the concept of weighted averages comes into play. In problems involving different rates (such as varied mpg values for different driving conditions), the total output (like total distance or total fuel consumption) is a weighted sum of the individual parts, requiring the establishment of an equation that accurately reflects these contributions.

Mixture Problems

Mixture problems involve two or more components that combine to form a final mixture with a known total, often requiring an analysis of the proportions of each component. In the context of fuel consumption with different efficiencies, the overall performance is determined by mixing the effects of driving conditions that yield varying rates, thereby necessitating a strategy to determine the contribution of each part.

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