Question

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

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

Define the fuel efficiency of the car

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

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.

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.

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: \(4x > 360\)

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: \(x > \frac{360}{4}\) \(x > 90\)

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.

Key concepts

Fossil Fuel Use

Fossil fuels are energy sources like coal, oil, and natural gas that have formed over millions of years from the remains of dead plants and animals. When we burn these fuels for energy, they release heat energy that powers cars, planes, and factories. However, this process also emits carbon dioxide (\(\mathrm{CO}_2\)), a greenhouse gas that contributes to climate change.
One important aspect of using fossil fuels is their efficiency in energy production. This term, known as 'energy efficiency,' refers to the amount of energy obtained from a specific amount of fossil fuel. In the context of the problem, we compare the energy efficiency of personal car travel with airplane travel to determine the best option for minimizing fossil fuel use and, consequently, carbon emissions. Choosing to drive a highly efficient car can sometimes result in significantly lower fossil fuel consumption compared to flying, depending on several factors such as the number of passengers and vehicle technology.
Ultimately, using fossil fuels more efficiently helps in reducing dependence on these finite resources and minimizes environmental impact. This is why calculating and comparing fuel efficiency across different travel methods is crucial, as seen in our exercise.

Carbon Emissions

Carbon emissions refer to the release of carbon, specifically in the form of carbon dioxide (\(\mathrm{CO}_2\)), into the atmosphere. This release happens primarily through the burning of fossil fuels, such as operating cars and airplanes. These emissions are a major contributor to global warming and climate change, as they trap heat in the atmosphere.
In the exercise, evaluating the carbon emissions entails looking at the amount of fuel each option (car or plane) uses since the fuel burned directly correlates with emissions produced. Since the efficiency of a vehicle determines the amount of fuel used, cars with higher miles per gallon are typically associated with lower emissions per mile traveled. The goal is to choose the travel method that minimizes these emissions, offering a more sustainable option.
Ultimately, finding ways to reduce carbon emissions is a global priority, and every choice, even choosing how to travel, adds up. Higher fuel efficiency not just means saving on fuel costs but also means contributing less to the global carbon footprint.

Fuel Efficiency Calculation

Fuel efficiency calculation is the process of determining how effectively a vehicle uses fuel to transport people or goods. It's often measured in miles per gallon (MPG) for cars. Higher MPG indicates better fuel efficiency, meaning the vehicle can travel more miles per gallon of fuel, thus using less fuel overall.
In the exercise, we calculate the total fuel efficiency of an airplane and compare it to that of a car. The airplane offers a fuel efficiency of 90 miles per gallon per passenger. For a group of four, this translates to a total of 360 miles per gallon. To determine the car's required efficiency, we set up an inequality (\(4x > 360\)). Solving for \(x\) (miles per gallon per person), we find that \(x > 90\), meaning that a car must exceed 90 MPG to use less fuel per person than an airplane.
Finding cars that meet this criterion can be challenging. While hybrid and electric cars often exceed this level of efficiency, traditional gasoline cars usually don't. Thus, understanding and applying fuel efficiency calculations can guide better decisions in reducing both fuel consumption and emissions.