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Chapter 1: Problem 38

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption 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: $$\begin{aligned}1 \text { U.K. gallon } &=4.5459631 \text { liters } \\\1 \text { U.S. gallon } &=3.7853060 \text { liters. }\end{aligned}$$ 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
The mistaken tourist thinks she needs 18.75 U.K. gallons (Step 2). The car actually requires 22.5143 U.S. gallons (Step 5).

Step by step solution

01

Determine the mistaken tourist calculation

First, calculate the number of gallons the mistaken tourist believes she needs based on the U.K. gallon fuel efficiency. The tourist believes the car鈥檚 fuel efficiency is 40 miles per gallon. For a 750-mile trip, divide the total miles by the fuel efficiency.
02

Perform the mistaken tourist calculation

The calculation is: \( \frac{750 \text{ miles}}{40 \text{ miles/gallon}} = 18.75 \text{ U.K. gallons} \). So, the mistaken tourist believes she needs 18.75 U.K. gallons.
03

Convert U.K. gallons to U.S. gallons

To find out the actual U.S. gallons needed, start by converting the U.K. gallons to liters (since 1 U.K. gallon = 4.5459631 liters), and then convert liters to U.S. gallons (since 1 U.S. gallon = 3.7853060 liters).
04

Convert 18.75 U.K. gallons to liters

Multiply 18.75 U.K. gallons by 4.5459631 liters per U.K. gallon: \( 18.75 \text{ U.K. gallons} \times 4.5459631 \text{ liters/U.K. gallon} = 85.237149 \text{ liters} \).
05

Convert liters to U.S. gallons

Divide the total liters by the number of liters in a U.S. gallon: \( \frac{85.237149 \text{ liters}}{3.7853060 \text{ liters/U.S. gallon}} = 22.5143 \text{ U.S. gallons} \). So, the car actually requires 22.5143 U.S. gallons.

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Key Concepts

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

Unit Conversion
Understanding unit conversion is critical when dealing with measurements in different systems. To accurately convert units, you will need to know the conversion factor between the units.
For example:
  • 1 U.K. gallon = 4.5459631 liters
  • 1 U.S. gallon = 3.7853060 liters
Conversion involves multiplying or dividing by these factors to switch from one unit to another. Always keep track of your units as you multiply or divide, making sure they cancel out correctly, leaving you with the desired unit.
Gallons to Liters
When you want to convert gallons (U.K. or U.S.) to liters, you use the conversion factor that relates gallons to liters.
For U.K. gallons to liters:
  • Multiply the number of U.K. gallons by 4.5459631 liters per U.K. gallon.
For U.S. gallons to liters:
  • Multiply the number of U.S. gallons by 3.7853060 liters per U.S. gallon.
These conversion factors arise from the defined relationship between gallons and liters in each system. This is useful, especially when dealing with fuel consumption and efficiency of cars advertised in different countries.
Fuel Efficiency Calculation
Fuel efficiency measures how far a vehicle can travel on a certain amount of fuel, usually expressed in miles per gallon (mpg).
To calculate fuel efficiency:
  • Divide the number of miles traveled by the amount of fuel used in gallons.
For example, if a car travels 750 miles and uses 18.75 U.K. gallons, its fuel efficiency is 750 miles divided by 18.75 U.K. gallons, equaling 40 miles per U.K. gallon.
This calculation helps you understand how much fuel your car consumes and plan for trips accordingly.
Miles per Gallon
Miles per gallon (mpg) is a key measure of a vehicle's fuel efficiency. It tells you how many miles a car can travel on one gallon of fuel.
For cars in the U.S., mpg is usually calculated using U.S. gallons. However, cars from other countries might use different standards.
  • To address differences: Convert the foreign unit of gallons to U.S. gallons before making comparisons.
In our example: The car advertises 40 miles per U.K. gallon. Converted to U.S. units, consider the actual number of gallons needed in the U.S. context, ensuring accurate mpg calculations. This avoids common mistakes in interpreting vehicle fuel efficiency from different regions.

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Most popular questions from this chapter

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