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Chapter 20: Problem 15

You and three friends want to take a trip together and are debating whether to fly or drive in a gasoline-powered car. In the context of fossil fuel energy use (and thus \(\mathrm{CO}_{2}\) emission), how good does the car's fuel efficiency need to be (in miles per gallon) in order for the driving option to use less fuel (per person) than would a fullyoccupied airplane, if the airplane gets 90 m.p.g. per passenger? Is it easy to find cars whose performance is at least this good?

Short Answer

Expert verified
Is it easy to find cars with this fuel efficiency? Answer: The minimum fuel efficiency a car needs to have is greater than 90 miles per gallon. It is easier to find hybrid and electric cars with this level of fuel efficiency, but it may not be as easy to find traditional gasoline-powered cars with this high fuel efficiency.

Step by step solution

01

Define the fuel efficiency of the car

Let \(x\) be the fuel efficiency of the car in miles per gallon.
02

Calculate the airplane's total fuel efficiency

Since the airplane gets 90 miles per gallon per passenger, we need to multiply that by the number of passengers which is 4 (you and your three friends). The total fuel efficiency of the airplane is \(4\times90=360\) miles per gallon.
03

Calculate the car's total fuel efficiency

Since there are 4 people in the car, the total fuel efficiency for the car would be \(4\times x=4x\) miles per gallon.
04

Compare the car's total fuel efficiency with the airplane's total fuel efficiency

For the car to use less fuel (per person) than the airplane, the car's total fuel efficiency needs to be greater than the airplane's total fuel efficiency: \(4x > 360\)
05

Solve for the fuel efficiency of the car

Divide both sides of the inequality by 4 to find the required fuel efficiency of the car: \(x > \frac{360}{4}\) \(x > 90\)
06

Determine if it is easy to find cars with the required fuel efficiency

The car's fuel efficiency needs to be greater than 90 miles per gallon for the driving option to use less fuel (per person) than a fully occupied airplane. There are some hybrid and electric cars on the market that can achieve this level of fuel efficiency, but it may not be as easy to find traditional gasoline-powered cars with this high fuel efficiency.

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