Problem 17 - Basic College Mathematics

Question

The 2017 Kia Optima LX does \(396 \mathrm{mi}\) of highway driving on 11 gal of gasoline. What is the mean number of miles expected per gallon-that is, what is the gas mileage?

Step-by-Step Solution

Answer

36 miles per gallon

Step 1: Identify the given values

Recognize the values provided in the problem: - Total distance driven: 396 miles- Total gallons of gasoline used: 11 gallons

Step 2: Understand the formula for gas mileage

The gas mileage, or mean number of miles per gallon, can be found by dividing the total distance driven by the total gallons of gasoline used. The formula is given by: \[ \text{Gas mileage} = \frac{\text{Total distance driven}}{\text{Total gallons of gasoline used}} \]

Step 3: Substitute the values into the formula

Plug in the given values into the gas mileage formula: \[ \text{Gas mileage} = \frac{396 \text{ miles}}{11 \text{ gallons}} \]

Step 4: Calculate the mean number of miles per gallon

Perform the division to find the gas mileage: \[ \text{Gas mileage} = \frac{396}{11} = 36 \text{ miles per gallon} \]

Key Concepts

Mean Number of Miles Per Gallon

To determine how efficiently a car uses fuel, we often calculate the mean number of miles per gallon (MPG). This measurement helps us understand the average distance a vehicle can travel on one gallon of gasoline, providing insight into its fuel efficiency. The formula to find the MPG involves dividing the total distance driven by the total gallons of gasoline used. For the 2017 Kia Optima LX example, the total distance is 396 miles, and the gasoline used is 11 gallons. By plugging these values into the formula, we get the gas mileage or MPG. This calculation reflects the car's average miles per gallon, giving us a clear view of its highway driving efficiency.

Division of Quantities

Understanding how to divide quantities is key to solving gas mileage problems. Division helps us spread a number across parts to find an average value or other useful measures. For instance, determining gas mileage requires dividing the total miles driven by the gallons of gasoline used. This division tells us how many miles the car can travel on one gallon of fuel. It's a simple division operation that yields critical information about the vehicle's performance. So in our example, we take 396 miles and divide it by 11 gallons. The result is \( \frac{396 \text{ miles}}{11 \text{ gallons}} = 36 \text{ miles per gallon} \). This division step is fundamental for understanding and calculating MPG.

Distance and Fuel Usage

Distance and fuel usage are two core components that determine a vehicle's fuel efficiency. Distance indicates how far the vehicle travels, while fuel usage tells us how much gasoline was consumed during that journey. Together, they help us assess overall performance. In our example with the 2017 Kia Optima LX, knowing that the car traveled 396 miles using 11 gallons of fuel gives us concrete data on its highway performance. By integrating these two values, we can compute the car's efficiency. Using the MPG formula, dividing the distance by fuel usage reveals that the car runs 36 miles per gallon. This concise metric allows easy comparison with other vehicles and helps in making fuel-efficient choices.