A sedan gets 12 mpg in the city and 18 mpg on the highway. If a driver drives a total of 420 mi

step 1 We have a sedan that goes 12 miles per gallon on the city and 18 miles per gallon on the highway

A sedan gets 12 mpg in the city and 18 mpg on the highway....

A sedan gets $12 \mathrm{mpg}$ in the city and $18 \mathrm{mpg}$ on the highway. If a driver drives a total of $420 \mathrm{mi}$ on 26 gal of gas, how many miles in the city and how many miles on the highway did he drive?

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Key Concepts

Weighted Average in Rate Problems

Weighted averages are used when different components contribute unevenly to a total. In the context of rate problems with varying fuel efficiencies, the overall measurement (such as total fuel consumption) is influenced by both the distance traveled in each condition and the differing consumption rates. This concept helps in determining the individual contributions from each segment when combined into a single overall outcome.

Fuel Efficiency

Fuel efficiency is a measure of how far a vehicle can travel per unit of fuel. It is typically expressed in miles per gallon (mpg) and is used to evaluate and compare the performance of different vehicles under various driving conditions. Understanding fuel efficiency is essential when assessing scenarios that involve varying consumption rates, such as city versus highway driving.

System of Linear Equations

A system of linear equations consists of multiple linear equations that are solved together to find a common solution for the unknown variables. In problems where there are multiple conditions — such as the total distance traveled and the total fuel consumption — setting up a system of equations allows you to relate these different variables and solve for them simultaneously.

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