Grady's station wagon gets 18 miles per gallon (mpg) in city...

Grady's station wagon gets 18 miles per gallon (mpg) in city driving and 24 mpg in highway driving. The car is driven $465 \mathrm{mi}$ on 23 gal of gasoline. How many miles were driven in the city and how many were driven on the highway?

Key Concepts

Rate Problems

Rate problems involve quantities that are consumed or produced over time or distance, connecting quantities like distance, time, and efficiency. They often require an understanding of unit rates, such as miles per gallon, and how these rates combine when different segments with different efficiencies are involved. This concept is crucial for translating real-world scenarios into mathematical models that can be solved using algebra.

Weighted Averages

Weighted averaging is used when different groups or components contribute differently to a total average. In the context of rate problems, different conditions can have different efficiencies, and the overall performance is influenced by the proportion of each contributing factor. Understanding weighted averages helps in breaking down the overall performance into parts based on their specific rates.

System of Linear Equations

This concept involves setting up and solving multiple equations that represent different constraints of a problem simultaneously. In problems like these, unknown quantities are represented by variables, and relationships provided in the problem statement are translated into equations. Solving the system allows for the determination of the values of these variables that satisfy all given conditions simultaneously.

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