Question

In Europe, cars' gas consumption is measured in liters per 100 kilometers. In the United States, the unit used is miles per gallon. a) How are these units related? b) How many miles per gallon does your car get if it consumes 12.2 liters per 100 kilometers? c) What is your car's gas consumption in liters per 100 kilometers if it gets 27.4 miles per gallon? d) Can you draw a curve plotting miles per gallon versus liters per 100 kilometers? If yes, draw the curve.

Short answer

#tag_title# Short Answer The relationship between liters per 100 kilometers and miles per gallon is given by the conversion formula: $$\text{MPG} = \frac{100 \times 0.621371}{\text{Liters per 100km} \times 0.264172}.$$ To convert from liters per 100km to miles per gallon, apply this formula. For example, given a car consumes 12.2 liters per 100 kilometers, it gets approximately 23.55 miles per gallon. To convert from miles per gallon to liters per 100 km, rearrange the conversion formula and substitute the given value. For example, given a car gets 27.4 miles per gallon, it consumes approximately 8.64 liters per 100 kilometers. The function relating miles per gallon and liters per 100 km is a hyperbolic curve, which can be plotted using graphing software or a graphing calculator.

Step-by-step solution

Conversion formula

To convert gas consumption from liters per 100 kilometers to miles per gallon, we can use the following formula: $$\text{MPG} = \frac{100 \times 0.621371}{\text{Liters per 100km} \times 0.264172}.$$ #b) Conversion from liters per 100 km to miles per gallon#

Calculate miles per gallon

Given that the car consumes 12.2 liters per 100 kilometers, we will use the conversion formula to find the miles per gallon: $$\text{MPG} = \frac{100 \times 0.621371}{12.2 \times 0.264172} \approx 23.55.$$ So, the car gets approximately 23.55 miles per gallon. #c) Conversion from miles per gallon to liters per 100 km#

Calculate liters per 100km

Given that the car gets 27.4 miles per gallon, we can rearrange the conversion formula to find the gas consumption in liters per 100 kilometers: $$\text{Liters per 100km} = \frac{100 \times 0.621371}{\text{MPG} \times 0.264172} \approx \frac{100 \times 0.621371}{27.4 \times 0.264172} \approx 8.64.$$ So, the car consumes approximately 8.64 liters per 100 kilometers #d) Drawing the curve#

Relationship between MPG and Liters per 100km

From the conversion formula: $$\text{MPG} = \frac{100 \times 0.621371}{\text{Liters per 100km} \times 0.264172}.$$ Rearranging for MPG, we get the following equation: $$\text{MPG} = \frac{1}{\text{Liters per 100km} \times 0.035274}.$$ This is a function of Liters per 100km which maps 0 to infinity as miles per gallon increases. So, we can draw a curve for this function. The curve can be plotted using graphing software (e.g., Desmos or a graphing calculator) by inputting the function or creating a table of values for various values of Liters per 100km and using those values to plot points on a graph showing MPG on the y-axis and Liters per 100km on the x-axis. The resulting curve will be a hyperbolic curve, with the two axes as asymptotes.

Key concepts

Liters per 100 Kilometers

Liters per 100 kilometers is a common measurement of fuel efficiency. It's frequently used in countries like those in Europe. When a car’s fuel consumption is quoted as a specific number of liters per 100 kilometers (L/100 km), it's referring to how many liters of fuel the car will burn to travel 100 kilometers. This measure gives drivers a clear understanding of how much fuel they will use over a standard distance.

Lower values of liters per 100 kilometers indicate better fuel efficiency, meaning the car needs less fuel to travel the same distance. For instance:

• If a car has a fuel consumption of 5 L/100 km, it means the car uses 5 liters of fuel for every 100 kilometers it travels.
• A car with 12 L/100 km consumes 12 liters for the same distance, indicating less fuel efficiency compared to the previous example.

Understanding liters per 100 kilometers helps drivers plan for fuel stops and manage fuel costs efficiently.

Miles per Gallon

In contrast to liters per 100 kilometers, miles per gallon (MPG) is a prevalent unit of measure for fuel economy in the United States. This metric tells you how many miles a vehicle can travel on one gallon of fuel. The higher the MPG, the more efficient the car is, as it can travel more miles per unit of fuel.

MPG provides an intuitive sense of a vehicle’s efficiency. Here's how it works:

• A car that gets 30 MPG can travel 30 miles on a single gallon of fuel.
• Conversely, a car with 15 MPG needs two gallons to cover the same distance implying it is less fuel-efficient.

Understanding MPG is essential for drivers aiming to optimize their fuel consumption and reduce their overall driving costs. It’s a straightforward method to evaluate vehicle performance concerning fuel economy.

Conversion Formula

Converting between liters per 100 kilometers and miles per gallon involves a specific formula that calculates these differing units of measurement by considering the conversion factors between miles, kilometers, liters, and gallons. The formula is as follows:

\[\text{MPG} = \frac{100 \times 0.621371}{\text{Liters per 100km} \times 0.264172}\]This formula allows you to input a vehicle's fuel consumption in liters per 100 kilometers and compute its equivalent in MPG.

If you know the MPG and seek to determine the equivalent liters per 100 kilometers, you rearrange the formula:

\[\text{Liters per 100km} = \frac{100 \times 0.621371}{\text{MPG} \times 0.264172}\]Utilizing these formulas helps car owners understand their vehicles’ fuel efficiency in different measurement systems, making it practical for international travel or exporting vehicles.

Graphing Software

Graphing software is a useful tool to visually display the relationship between liters per 100 kilometers and miles per gallon. These graphical representations can illuminate how changes in one measure affect the other.

To plot this relationship, input the conversion formula into graphing applications like Desmos or any standard graphing calculator:

• Assign liters per 100 kilometers values for the x-axis.
• Calculate the corresponding MPG using the conversion formula for the y-axis.
• Plot these values to create a curve.

The curve appears hyperbolic, showcasing that as fuel efficiency increases in one metric, it affects the other reciprocally. Such visual aids enhance understanding, allowing learners to quickly appreciate how small adjustments in one measurement can lead to significant changes in fuel efficiency.