Problem 18 - Basic College Mathematics

Question

The 2017 Chevrolet Malibu with a 1.5 \(\mathrm{L}\) engine does \(243 \mathrm{mi}\) of city driving on \(9 \mathrm{gal}\) of gasoline. What is the mean number of miles expected per gallon \(-\) that is, what is the gas mileage?

Step-by-Step Solution

Answer

The gas mileage is 27 miles per gallon.

Step 1 - Identify Key Information

Identify the key pieces of information given in the problem: 1. Distance traveled: 243 miles 2. Amount of gasoline used: 9 gallons

Step 2 - Understand the Formula for Gas Mileage

To find the gas mileage (miles per gallon), use the formula: Gas Mileage = \(\frac{\text{Distance Traveled}}{\text{Gallons of Gasoline Used}}\)

Step 3 - Plug in the Values

Substitute the given values into the formula: Gas Mileage = \(\frac{243 \text{ miles}}{9 \text{ gallons}}\)

Step 4 - Calculate the Gas Mileage

Perform the division to find the mean number of miles per gallon: Gas Mileage = \(\frac{243}{9} = 27 \text{ miles per gallon}\)

Key Concepts

Gas Mileage Formula

Understanding how to calculate gas mileage, also known as fuel efficiency, is vital for determining how far a vehicle can travel on a given amount of gasoline. Gas mileage is expressed in miles per gallon (mpg) and is calculated using a simple formula:

Gas Mileage = \(\frac{ \text{Distance Traveled} }{ \text{Gallons of Gasoline Used} } \)

This formula helps us understand the relationship between the distance a car travels and the amount of fuel consumed. For instance, with the 2017 Chevrolet Malibu example, the car traveled 243 miles using 9 gallons of gasoline. By substituting these values into the formula, we get:

Gas Mileage = \(\frac{243 \text{ miles}}{9 \text{ gallons}} \)

Simplifying this fraction results in a gas mileage of 27 miles per gallon.

Basic Arithmetic

Basic arithmetic is a cornerstone of problem-solving in mathematics. In the context of calculating gas mileage, we use division to find our answer. Here's a quick refresher:

Division is one of the four fundamental arithmetic operations. It calculates how many times one number (the divisor) is contained within another (the dividend). For our gas mileage calculation, we performed the following division:

243 ÷ 9

To solve this, you determine that 9 fits into 243 exactly 27 times. Thus, 243 ÷ 9 equals 27. In our problem, this means the car travels 27 miles for each gallon of gasoline used.

Distance-Rate-Time Problems

Distance-rate-time problems are common in mathematics and involve relating distance traveled, the rate of travel, and the time taken. The basic formula for these problems is:

Distance = Rate × Time

When dealing with gas mileage, the concept shifts slightly but still involves these principles. Instead of time, we are focused on fuel (gasoline) consumption. Essentially, we are looking for the 'rate' of distance per unit of gasoline, which is why we use the formula:

Gas Mileage = \(\frac{ \text{Distance} }{ \text{Gallons} } \)

This allows us to find out how efficiently a vehicle uses fuel—a vital factor for both economic and environmental considerations.