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Chapter 5: Problem 10

A 2017 Ford F-150 6 -cylinder will travel \(297 \mathrm{mi}\) on 13.5 gal of gasoline in highway driving. What is the rate in miles per gallon?

Short Answer

Expert verified
The rate is 22 miles per gallon.

Step by step solution

01

Identify the given values

The problem provides two key values: the distance traveled and the amount of gasoline used. Here, the distance is 297 miles, and the gasoline used is 13.5 gallons.
02

Set up the formula

The rate in miles per gallon (mpg) is calculated using the formula: \[\text{mpg} = \frac{\text{miles}}{\text{gallons}}\]
03

Substitute the given values into the formula

Substitute 297 miles for the distance and 13.5 gallons for the gasoline used: \[\text{mpg} = \frac{297 \text{ mi}}{13.5 \text{ gal}}\]
04

Perform the division

Divide 297 by 13.5 to find the rate: \[\text{mpg} = \frac{297}{13.5} \approx 22 \text{ mpg}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

unit rate
In this exercise, we are asked to determine the rate in miles per gallon (mpg). This is a perfect example of finding a unit rate. A unit rate is a ratio that compares two different measurements with one of the terms being 1. Here, we are comparing miles traveled to gallons of gasoline. Our goal is to find out how many miles the truck can travel per one gallon of gasoline. This helps us understand efficiency and consumption in real-world situations. Unit rates are common and useful in various scenarios, from tracking speed to evaluating costs per item, making it an essential concept to grasp.
division
Division is key to solving this problem. We use it to find how many miles the truck travels per gallon of gasoline. By dividing total miles by the total gallons used, you isolate the value for one gallon.

Division simplifies our understanding. Instead of knowing how far a vehicle travels on a full tank, we break it down. This way, we can easily multiply the result by any number of gallons to predict the distance. For instance, if our truck gets 22 miles per gallon, then with 10 gallons, it will drive around 220 miles. Ensuring competence in division will aid numerous problem-solving scenarios.
problem-solving steps
Let鈥檚 break down the problem-solving steps for better understanding:

  • Identify given values: Recognize the information provided by the problem. Here, we have 297 miles driven and 13.5 gallons of gasoline used.
  • Set up the formula: Use the appropriate formula. In this case, mpg = miles/gallons.
  • Substitute the values: Place the given values into the formula: mpg = 297 miles / 13.5 gallons.
  • Perform the division: Divide 297 by 13.5 to find 22 mpg.

Following these steps ensures that you methodically tackle the problem. Remembering and applying these steps can make solving similar problems straightforward and less daunting.
fuel efficiency
Fuel efficiency, measured in miles per gallon (mpg), is a critical metric for understanding a vehicle's performance. Higher mpg means a vehicle can travel further on a single gallon of gas, indicating better fuel efficiency. This not only saves you money but also reduces environmental impact. For instance, a 22 mpg rating means the truck performs reasonably well on highways. Keep in mind that factors such as driving behavior, road conditions, and vehicle maintenance can influence actual fuel efficiency. Understanding and striving for higher fuel efficiency is beneficial for both economic and environmental reasons.

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