Question

An average vehicle puts out nearly 20 lbm of carbon dioxide into the atmosphere for every gallon of gasoline it burns, and thus one thing we can do to reduce global warming is to buy a vehicle with higher fuel economy. A U.S. government publication states that a vehicle that gets 25 rather than 20 miles per gallon will prevent 10 tons of carbon dioxide from being released over the lifetime of the vehicle. Making reasonable assumptions, evaluate if this is a reasonable claim or a gross exaggeration.

Short answer

Answer: The claim is reasonable.

Step-by-step solution

Establish the facts

The average vehicle emits 20 pounds of CO2 per gallon of gasoline it burns. Claims: A. A 25 MPG vehicle's total CO2 emissions over its lifetime is 10 tons less than that of a 20 MPG vehicle. B. 10 tons of CO2 equals 20,000 pounds.

Convert tons to pounds

To get everything in the same units, convert 10 tons of CO2 to pounds: 10 tons × 2000 pounds/ton = 20,000 pounds CO2

Calculate the total number of gallons consumed over a lifetime

We are given that the lifetime difference in CO2 emissions between vehicles is 20,000 pounds. With 20 pounds of CO2 per gallon of gasoline burned, we can determine the lifetime difference in the number of gallons burned: 20,000 pounds CO2 ÷ 20 pounds/gallon = 1,000 gallons

Determine the Lifetime Difference in Miles Driven for 20 MPG and 25 MPG Vehicles

Let x represent the total number of miles driven in a vehicle's lifetime. For a 20 MPG and a 25 MPG vehicle, we can determine the total number of gallons of fuel consumed over this distance: 20 MPG vehicle: x/20 gallons 25 MPG vehicle: x/25 gallons

Calculate the difference in gallons consumed

Using the values from step 3 and step 4, set up and solve for the difference in the number of gallons of fuel consumed: x/20 - x/25 = 1,000 (5x - 4x) / 100 = 1,000 x = 100,000

Validate the claim

In this case, the total number of miles driven over the lifetime of both vehicles is 100,000. For 20 MPG and 25 MPG vehicles: Total CO2 emissions for a 20 MPG vehicle: 100,000 miles / 20 MPG × 20 pounds/gallon = 100,000 pounds CO2 Total CO2 emissions for a 25 MPG vehicle: 100,000 miles / 25 MPG × 20 pounds/gallon = 80,000 pounds CO2 The difference in CO2 emissions over the lifetime of the vehicles: 100,000 pounds - 80,000 pounds = 20,000 pounds, or 10 tons. The claim in the publication is therefore reasonable as the difference in CO2 emissions between the two fuel economies matches the given difference of 10 tons over the lifetime of a vehicle.