Fuel Efficiency, Rates and Linear Modeling Lab
Name(s):
Instructions: Answer all questions below. You may work with a partner and only need to turn in one
set of answers for both people. Just be sure that both names are listed above. Show all work in the space
provided for each question.
Materials: A laptop, a sheet of graph paper, and a calculator.
1. Suppose you drive a car that has a fuel efficiency of 25 miles per gallon (mpg) for highway driving.
The gas tank in your car holds a total of 15 gallons.
(a) If you drive 50 miles, how much gas do you use?
(b) How far can you drive on one tank of gas?
1
(c) How much gas do you use in 15 minutes if you drive at a uniform speed of 65 miles per hour?
(Hint: you’ll need to do some unit conversion and this problem will require a couple steps.)
2. In a Toyota Prius, there is a screen on the dashboard titled ”Consumption” which shows your average
fuel efficiency in 5 minute intervals. The screen looks like this:
(a) By reading the graph, estimate the average fuel efficiency shown in the 15-20 minute interval.
2
(b) What, if anything, does the area of the bars represent?
(c) By using this graph, can you determine the amount of fuel consumed? If not, what additional
information would you need to know?
(d) Suggest a better way to graph fuel consumption using a different variable on the x-axis and/or
y-axis. Explain your reasoning.
3
3. Use the available computers to look up and choose one hybrid and one non-hybrid model vehicle. The
two vehicles need not be the same make or the same style car, but the hybrid needs to be the more
expensive vehicle (otherwise the questions below will be pointless!).
(a) Find the Manufacturer’s Suggested Retail Price (MSRP) for both vehicles. List the MSRPs here.
(b) Find the gas mileage (mpg rating) for city driving or highway driving for both vehicles. You can
use either the city or highway value for the questions to follow, but you must make the same
choice for both vehicles. That is, if you choose the city mileage for the hybrid, you must also
choose the city mileage for the non-hybrid. List the gas mileages here.
4. Let’s assume the price of gas is $2.60 per gallon.
(a) Determine a linear equation expressing the cost of the vehicle after driving x miles. You can ignore
any maintenance and other costs such as insurance and taxes; only consider the MSRP and the
fuel efficiency. Write the equations for both vehicles here. (Hint: consider what the y-intercept
should be and what units the slope should have.)
4
(b) Using algebra, determine when the cost of the two vehicles will be the same. Show your work and
state your answer in a complete sentence.
(c) Using graph paper, graph the cost functions for both vehicles together on the same plot from x=0
to x=200,000 miles. Clearly label the axes and draw the lines carefully using a straightedge.
(d) Examine your graph. Where do the lines intersect? What does this point represent? State your
answers in complete sentences.
(e) If you drive 15 thousand miles per year, how many years must you own a hybrid before it starts
to save you money?
5
5. Now suppose you are dedicated to being “carbon neutral” by purchasing carbon credits to offset your
emissions. Go to the following website to calculate the cost of carbon credits for both vehicles assuming
that you drive 15 thousand miles per year: http://www.treehuggerenergy.com.
(a) The website linked will give you the cost per month for the carbon credits. Use this information
to calculate the cost per mile driven for both vehicles. Show your work.
(b) Write down new equations for the cost of each vehicle including the cost of the carbon credits.
(c) Now, determine how many miles you must drive before the hybrid starts to save you money.
(d) How many years must you own the hybrid before it starts to save you money?
6