Question

In recent years, there has been a large push for an increase in the use of renewable resources to produce the energy we need to power our vehicles. One of the newer fuels that has become more widely available is a mixture of \(85 \%\) ethanol and \(15 \%\) gasoline, E85. Despite being more environmentally friendly, one of the potential drawbacks of E85 fuel is that it produces less energy than conventional gasoline. Assume a car gets \(28.0 \mathrm{mi} / \mathrm{gal}\) using gasoline at \(\$ 3.50 / \mathrm{gal}\) and \(22.5 \mathrm{mi} / \mathrm{gal}\) using \(\mathrm{E} 85\) at \(\$ 2.85 / \mathrm{gal}\). How much will it cost to drive 500 . miles using each fuel?

Short answer

For gasoline, it will cost approximately \$62.51 to drive 500 miles, whereas for E85 fuel, it will cost approximately \$63.33. Hence, E85 fuel is slightly more expensive for driving the same distance despite its environmental benefits.

Step-by-step solution

Calculate the gallons of fuel needed for 500 miles for each type of fuel

To find out how many gallons of fuel are needed, divide the total distance (500 miles) by the miles per gallon for each fuel type. For gasoline: \(\frac{500 \ \mathrm{miles}}{28 \ \mathrm{mi/gal}}\) For E85: \(\frac{500 \ \mathrm{miles}}{22.5 \ \mathrm{mi/gal}}\)

Compute the gallons of fuel for each type

Now, let's do the calculations: For gasoline: \(\frac{500}{28} = 17.86 \ \mathrm{gal}\) (approx.) For E85: \(\frac{500}{22.5} = 22.22 \ \mathrm{gal}\) (approx.)

Calculate the cost of driving 500 miles using each type of fuel

To find the cost, multiply the total gallons of fuel needed by the cost per gallon for each fuel type. For gasoline: \(17.86 \ \mathrm{gal} \times \$3.50 /\mathrm{gal}\) For E85: \(22.22 \ \mathrm{gal} \times \$2.85 /\mathrm{gal}\)

Compute the cost for each type of fuel

Now, let's do the calculations: For gasoline: \(17.86 \times \$3.50 = \$62.51\) For E85: \(22.22 \times \$2.85 = \$63.33\)

Comparing the costs

After calculating the costs, we find out that it will cost: - \$62.51 to drive 500 miles using gasoline - \$63.33 to drive 500 miles using E85 fuel So, it will cost slightly more to drive 500 miles using E85 fuel, despite it being more environmentally friendly.

Key concepts

Ethanol Fuel

Ethanol fuel is a type of renewable energy made primarily from corn or sugarcane. Compared to conventional gasoline, ethanol is considered more environmentally friendlier because it reduces greenhouse gas emissions. It's typically mixed with gasoline to create fuels such as E10 and E85, where the number indicates the percentage of ethanol in the blend.

E85 fuel, which contains 85% ethanol, is becoming popular as an alternative fuel for vehicles. However, using ethanol can result in lower fuel efficiency. This means that cars running on E85 might not travel as far as they would on traditional gasoline, affecting the overall cost and experience of using this type of fuel.

In summary, while ethanol fuels like E85 are better for the environment, they may not always be the most cost-effective choice in terms of fuel efficiency.

Energy Efficiency

Energy efficiency in vehicles refers to how effectively a vehicle converts fuel into distance traveled. In our current context, E85 fuel provides lower energy efficiency compared to conventional gasoline. This is because ethanol has a lower energy content per gallon than gasoline.

When comparing the two for a journey, it becomes evident that a car using E85 will require more fuel (in gallons) than a car using gasoline to cover the same distance.

• The car gets 28 miles per gallon (mpg) on gasoline.
• On E85, it only achieves 22.5 mpg.

This difference highlights why, despite E85 being cheaper per gallon, the total cost to travel the same number of miles can be greater than using regular gasoline.

Understanding energy efficiency is crucial when considering different fuels, as it affects not only cost but also overall fuel consumption and environmental impact.

Fuel Cost Analysis

Fuel cost analysis involves comparing the costs associated with using different types of fuels over a specified distance. In our exercise, the goal was to understand the cost implications of driving 500 miles with gasoline versus E85.

To undertake a fuel cost analysis, we must first calculate the number of gallons needed for the trip by dividing the total distance by the vehicle's fuel efficiency (measured in miles per gallon). After obtaining the total gallons needed, we multiply by the fuel cost per gallon to get the total fuel cost.

• For gasoline: 17.86 gallons needed multiplied by $3.50 per gallon results in approximately $62.51.
• For E85: 22.22 gallons needed multiplied by $2.85 per gallon results in approximately $63.33.

Through this analysis, we discover that despite E85's lower price per gallon, it costs slightly more to fuel the trip compared to gasoline due to its lower energy efficiency. This illustrates how fuel cost analysis can help consumers make informed decisions about their fuel choices based on both financial cost and environmental considerations.