/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 Your car's gas tank is full and ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 3

Your car's gas tank is full and you take a trip. You travel 212 miles, then you fill your gas tank up again and it takes 10.8 gallons. If you designate your change in distance as 212 miles and your change in gallons as 10.8 , what is the average rate of change of gasoline used, measured in miles per gallon?

Short Answer

Expert verified
19.63 miles per gallon

Step by step solution

01

Identify the Variables

The change in distance, \(\triangle d\), is 212 miles, and the change in gasoline, \(\triangle g\), is 10.8 gallons.
02

Write the Formula for Average Rate of Change

The average rate of change can be calculated using the formula: \[ \text{Average Rate of Change} = \frac{\triangle d}{\triangle g} \]
03

Substitute the Values into the Formula

Plug in \( \triangle d = 212 \text{ miles} \) and \( \triangle g = 10.8 \text{ gallons} \) into the formula: \[ \text{Average Rate of Change} = \frac{212}{10.8} \]
04

Calculate the Result

Perform the division: \[ \text{Average Rate of Change} = \frac{212}{10.8} \approx 19.63 \text{ miles per gallon} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Distance
In the context of the given exercise, distance refers to how far you travel during your trip. Here, the distance is specified as 212 miles. Distance is an important variable when calculating rates such as miles per gallon. To break it down:
  • The distance you travel is the numerator in the average rate of change formula.
  • Distance is usually measured in units like miles, kilometers, or meters.
Knowing your total distance can help you understand your travel efficiency. The more miles you cover with the same amount of gasoline, the more efficient your travel is in terms of fuel consumption.
Gasoline Consumption
Gasoline consumption is the amount of fuel your car uses over a given distance. In this exercise, you refill your tank with 10.8 gallons of gasoline after traveling 212 miles.
  • Gasoline consumption is the denominator in the average rate of change formula.
  • It's generally measured in gallons or liters.
Understanding how much gasoline your car consumes is crucial for calculating efficiency.
For example, knowing you used 10.8 gallons over a distance of 212 miles helps you determine your car鈥檚 fuel efficiency in miles per gallon (mpg).
Miles per Gallon
Miles per gallon (mpg) measures your car鈥檚 fuel efficiency. It's calculated as the average rate of change of gasoline used. This metric tells you how many miles your car can travel per gallon of gasoline. To find it, use the formula: \[ \text{Average Rate of Change} = \frac{\triangle d}{\triangle g} \] Where:
  • \[ \triangle d \] = Change in distance (212 miles in this case)
  • \[ \triangle g \] = Change in gasoline (10.8 gallons in this case)
Substituting the values: \[ \text{Average Rate of Change} = \frac{212}{10.8} \] Performing the division: \[ \text{Average Rate of Change} \approx 19.63 \text{ miles per gallon} \] Understanding your vehicle鈥檚 miles per gallon helps you gauge its fuel efficiency and plan for trips, budget for fuel costs, and understand the environmental impact of your driving.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

a. Write an equation for the line parallel to \(y=2+4 x\) that passes through the point (3,7) . b. Find an equation for the line perpendicular to \(y=2+4 x\) that passes through the point (3,7) .

According to the U.S. Burcau of the Census, the percentage of persons 25 years old and over completing 4 or more years of college was 4.6 in 1940 and 27.6 in 2005 . a. Plot the data, labeling both axes and the coordinates of the points. b. Calculate the average rate of change in percentage points per year. c. Write a topic sentence summarizing what you think is the central idea to be drawn from these data.

Consider the function \(f(x)=4\). a. What is \(f(0) ? f(30) ? f(-12.6) ?\) b. Describe the graph of this function. c. Describe the slope of this function's graph.

Find the equation of the line in the form \(y=m x+b\) for each of the following sets of conditions. Show your work. a. Slope is \(\$ 1400 /\) year and line passes through the point \((10 \mathrm{yr}, \$ 12,000)\) b. Line is parallel to \(2 y-7 x=y+4\) and passes through the point (-1,2) c. Equation is \(1.48 x-2.00 y+4.36=0 .\) d. Line is horizontal and passes through ( 1.0,7.2 ). e. Line is vertical and passes through ( 275,1029 ). \(\mathbf{f}\). Line is perpendicular to \(y=-2 x+7\) and passes through (5,2)

Given the function \(Q(t)=13-5 t,\) construct a related function whose graph: a. Lies five units above the graph of \(Q(t)\) b. Lies three units below the graph of \(Q(t)\) c. Has the same vertical intercept d. Has the same slope e. Has the same steepness, but the slope is positive
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.