/*! 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 39 A tourist purchases a car in Eng... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 39

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel con- sumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon: $$ \begin{gathered} \text { 1 U.K. gallon }=4.5460900 \text { liters } \\ \text { 1 U.S. gallon }=3.785411 \text { 8 liters. } \end{gathered} $$ For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

Short Answer

Expert verified
(a) 18.75 U.K. gallons; (b) 22.53 U.S. gallons.

Step by step solution

01

Convert Miles to Gallons (Mistaken Tourist)

The tourist believes the car operates at 40 miles per U.K. gallon. For a trip of 750 miles, the tourist calculates the fuel needed by dividing the total miles by the fuel consumption rate:\[ \text{Gallons needed (mistaken)} = \frac{750 \text{ miles}}{40 \text{ miles/gallon}} \]This calculation gives:\[ \text{Gallons needed (mistaken)} = 18.75 \text{ U.K. gallons} \]
02

Convert U.K. Gallons to U.S. Gallons (Real Conversion)

1 U.K. gallon is 4.5460900 liters and 1 U.S. gallon is 3.7854118 liters. To find out how many U.S. gallons the 18.75 U.K. gallons is equivalent to, we first convert U.K. gallons to liters, and then convert liters to U.S. gallons:\[ 18.75 \text{ U.K. gallons} \times 4.5460900 \text{ liters/U.K. gallon} = 85.2356875 \text{ liters} \]Now convert liters to U.S. gallons:\[ 85.2356875 \text{ liters} \div 3.7854118 \text{ liters/U.S. gallon} = 22.5262 \text{ U.S. gallons} \]Thus, the car actually requires approximately 22.53 U.S. gallons for a 750-mile trip.

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.

Fuel Efficiency
Fuel efficiency determines how well a vehicle uses fuel to travel a distance. Typically, it's measured as the number of miles traveled per gallon of fuel. In the exercise, the car has a listed fuel efficiency of 40 miles per gallon. This means that for every gallon of fuel, the car can travel 40 miles.
  • Higher fuel efficiency indicates a vehicle that uses less fuel to travel the same distance, which is more cost-effective and environmentally friendly.
  • Fuel efficiency is crucial for budgeting fuel costs, trip planning, and reducing carbon emissions.
For the tourist traveling 750 miles, understanding fuel efficiency helps calculate how many gallons of fuel the car is expected to use. They assume 18.75 gallons, based on their fuel efficiency estimate using the UK gallon. This highlights the importance of knowing the correct unit of measurement when calculating fuel needs.
Metric System Conversion
Metric system conversion involves changing measurements from one system to another, essential when dealing with international units. Here, we need to convert gallons between UK and US measurements, which involves understanding the liter conversion.
  • 1 U.K. gallon = 4.5460900 liters
  • 1 U.S. gallon = 3.7854118 liters
First, convert 18.75 U.K. gallons into liters by multiplying by the conversion factor (4.5460900 liters per U.K. gallon). This results in 85.2356875 liters.
Next, convert these liters into U.S. gallons by dividing by the U.S. gallon conversion factor (3.7854118 liters per U.S. gallon). This provides an accurate fuel requirement of approximately 22.53 U.S. gallons. This step is crucial, as it corrects the tourist's initial assumption, showing the power of metric conversions.
UK to US Measurement Differences
Understanding the differences between UK and US measurements helps prevent miscalculations and unnecessary surprises. The exercise demonstrates a practical example of these differences where gallons are not the same in both countries.
  • The UK gallon is larger than the US gallon, primarily because the measuring systems developed independently.
  • Recognizing these distinctions is vital when using vehicles or goods crossing international boundaries.
The mistaken tourist initially used the UK gallon assumptions, leading them to underestimate the needed fuel in the US. By converting to the US gallon, they learn the car actually requires more fuel (22.53 U.S. gallons versus the expected 18.75 UK gallons).
This highlights the necessity of verifying units and conversions when dealing with international products.

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

Gold, which has a density of \(19.32 \mathrm{~g} / \mathrm{cm}^{3}\), is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold, with a mass of \(27.63 \mathrm{~g}\), is pressed into a leaf of \(1.000 \mu \mathrm{m}\) thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius \(2.500\) \(\mu \mathrm{m}\), what is the length of the fiber?

(a) A unit of time sometimes used in microscopic physics is the shake. One shake equals \(10^{-8} \mathrm{~s}\). Are there more shakes in a second than there are seconds in a year? (b) Humans have existed for about \(10^{6}\) years, whereas the universe is about \(10^{10}\) years old. If the age of the universe is defined as 1 "universe day," where a universe day consists of "universe seconds" as a normal day consists of normal seconds, how many universe seconds have humans existed?

A unit of area often used in measuring land areas is the hectare, defined as \(10^{4} \mathrm{~m}^{2}\). An open-pit coal mine consumes 75 hectares of land, down to a depth of \(26 \mathrm{~m}\), each year. What volume of earth, in cubic kilometers, is removed in this time?

Iron has a density of \(7.87 \mathrm{~g} / \mathrm{cm}^{3}\), and the mass of an iron atom is \(9.27 \times 10^{-26} \mathrm{~kg}\). If the atoms are spherical and tightly packed, (a) what is the volume of an iron atom and (b) what is the distance between the centers of adjacent atoms?

The common Eastern mole, a mammal, typically has a mass of \(75 \mathrm{~g}\), which corresponds to about \(7.5\) moles of atoms. (A mole of atoms is \(6.02 \times 10^{23}\) atoms.) In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole?
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Energy Physics

Read Explanation

Linear Momentum

Read Explanation

Solid State Physics

Read Explanation

Medical Physics

Read Explanation

Rotational Dynamics

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.