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Mileage Logger

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									Homework Assignment: “I can’t drive 55!”                        Name:____________________
By Claudia Bode1, Alan Gleue2 and Carolyn Pearson3
1
 University of Kansas, Lawrence, KS, 2Lawrence High School, and 3Bonner Springs High School

This weekend, you and your friends are planning to take a road trip. The destination is 100 miles away.
The time it takes to travel this distance depends on the speed of the car. Fill out the data table below
using a graphing program such as Logger Pro or Excel to help you make the calculations. Use your
results to answer the questions that follow.

                           Speed           Distance          Time           Time
                      (miles per hour)      (miles)       (in hours)    (in minutes)
                              5              100
                             10              100
                             15              100
                             20              100
                             25              100
                             30              100
                             35              100
                             40              100
                             45              100
                             50              100
                             55              100
                             60              100
                             65              100
                             70              100
                             75              100
                             80              100
                             85              100

Part I - Questions Using the Data Table
(a) How many hours does it take to drive 100 miles at 10 miles per hour? _______________________
(b) How many hours does it take to drive 100 miles at 20 miles per hour? ________________________
(c) How much time is saved by driving 20 mph instead of 10 mph (a doubling of your speed)? _________
(d) How many hours does it take to drive 100 miles at 25 miles per hour? ________________________
(e) How many hours does it take to drive 100 miles at 50 miles per hour? ________________________
(f) How much time is saved by driving 50 mph instead of 25 mph (a doubling of your speed)? ________
(g) How many hours does it take to drive 100 miles at 40 miles per hour? _______________________
(h) How many hours does it take to drive 100 miles at 80 miles per hour? ______________________
(i) How much time is saved by driving 80 mph instead of 40 mph (a doubling of your speed)? ________
(j) What happens to the time saved as you double your velocity at faster speeds? _______________
_____________________________________________________________________________________


[I can’t drive 55!]                                                                         [Page 1 of 5]
Part II - Plot the Data and Analyze the Graphs

To visualize how time savings changes with increasing speeds, plot the data from Part I. Your graph
should have speed (miles per hour) on the x axis and time (hr) on the y axis. Make sure to print the
graphs.

(a) Which of the four basic types of graphs (direct or linear; inverse or indirect; top-opening parabola;
and side-opening parabola) best models the data on your graph? ______________________________

(b) What is the constant of proportionality? ________________________

(c) What are the units for this constant of proportionality? ________________

(d) Write the equation using the variables on the graph: ______________________________________

(e) Now linearize the graph. Explain how to do this: _________________________________________

(f) Why is it helpful to linearize the graph? _________________________________________________

(g) What is the slope of the linearized graph (give number and units): ___________________________

(h) How does this compare to the constant of proportionality? _________________________________

(i) Give the linearized equation in y = mx + b format by using the variables as displayed on the graph:

_____________________________________________________________________________________

(j) How does this compare to the equation you wrote in question d above? ________________________


Part III - Should We Decrease the Maximum Speed Limit?
                           Remember the record high gas prices during the summer of 2008? With
                           prices topping $4 per gallon in some locations, U.S. Senator John Warner
                           suggested that congress should consider reducing speed limits on US
                           highways [1, 2]. Senator Warner wanted to make sure that speed limit laws
                           provide optimum gasoline efficiency. This idea is not new. Back in the 1970s
and 1980s, almost all roads had a 55 mph maximum speed. This widely unpopular law was passed in
1974 in response to the 1973-1974 oil crisis [3]. The goal was to reduce gasoline consumption and also
save lives [4]. The law was repealed in 1995 when oil was inexpensive and abundant. Today, oil prices
are volatile, demand is growing and the supply is decreasing.
Links for more information:
1. http://www.politico.com/news/stories/0708/11525.html
2. http://www.bloggingstocks.com/2008/07/07/u-s-sen-john-warner-talks-up-55-mph-national-speed-
limit/
3. http://en.wikipedia.org/wiki/55_mph
4. http://www.treehugger.com/files/2008/02/55_mph_its_time.php


[I can’t drive 55!]                                                                           [Page 2 of 5]
(a) What's your view? Should the U.S. Congress pass a 55 mph or 60 mph national speed limit to save
gasoline and lives? Or is this another example of government interfering with your personal freedom /
liberty? Let me know what you think.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________


One disadvantage of reducing the speed limit is the extra travel time. As Homer Simpson argued, “Sure,
they'll save a few lives. But, millions will be late!” Look back at your data table and/or graph to help you
answer the following questions.

(b) How long (in minutes) would it take you to drive 100 miles if you drove at 70 mph? _____________

(c) How long (in minutes) would it take you to drive 100 miles if you drove at 60 mph? _____________

(d) What is the difference in minutes by driving at this lower speed? ____________________________

(e) So it takes more time to get places at slower speeds. Hmmm. That’s a disadvantage. What would
you say are the advantages of driving slower?

_____________________________________________________________________________________

_____________________________________________________________________________________

(f) If the designated speed limit is 70 mph, how many minutes will you save by driving the 100 mile
distance at 5 mph over the speed limit? Is it worth it?
_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________

Part IV - The Speedometer “Sweet Spot”

How fast you drive affects your car’s fuel mileage. This is a fairly complicated subject, but many cars are
the most efficient between 40 and 60 mph (see: http://auto.howstuffworks.com/question4771.htm;
and http://www.mpgforspeed.com/). At faster speeds, mileage begins to drop off and your car
becomes less efficient. To get the best mileage, you should drive your car in the “sweet spot.”



[I can’t drive 55!]                                                                            [Page 3 of 5]
Take a look at the following graph taken from the fueleconomy.gov website:
(http://fueleconomy.gov/feg/driveHabits.shtml)

This graph shows a vehicle that gets around 29 mpg
at 60 mph and makes around 23 mpg at 75 mph.
This car’s “sweet spot” for fuel efficiency is
between 40 and 55 mph.




(a) Let’s say you commute 30 miles a day in the car used to calculate the data for the graph above.
Refer to this graph to complete the following table and questions. Round your answers to the nearest
hundredth. Assume gas costs $4 per gallon.

  Speed         Mileage      Time to drive      Gallons of gas to       Cost/Day           Cost/Year
  (mph)          (mpg)       30 miles (min)      drive 30 miles        (roundtrip)        (roundtrip)
    60
    75



(b) How much time would be saved by driving 75 mph instead of 60 mph for this 30 mile commute?
___________

(c) How much money would be saved per year by driving 60 mph instead of 75 mph? _______________

(d) If this was your situation, which speed would you drive during your daily commute and why?

_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________


Part V - Saving Lives

There are typically around 38,000 to 40,000 traffic fatalities per year nationally. A research study
announced in 2008 indicated that as gasoline becomes more expensive, people drive less and drive
slower to save gas. This results in fewer automobile fatalities. This study found that there could be as
many as 12,000 fewer deaths per year nationally when gas prices top $4 per gallon. See this link for



[I can’t drive 55!]                                                                          [Page 4 of 5]
more information:
http://www.usatoday.com/money/autos/2008-07-11-auto-deaths-gas-prices-study_N.htm.

(a) In 2006, there were 468 traffic fatalities in Kansas and a total of 42,708 traffic fatalities nationally
(data from: http://www-fars.nhtsa.dot.gov/States/StatesFatalitiesFatalityRates.aspx). Assuming the
research study described above is valid, estimate how many fewer fatalities we might expect to see in
the state of Kansas if gas prices rise above $4 per gallon? Come up with an answer and justify it
mathematically.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

OK, you’ve done some good work in this activity. You’ve practiced making an inverse graph and then
linearizing it. You looked at how different speeds affect travel time, gasoline efficiencies and traffic
fatalities. Make sure you:

       Print both your inverse graph and your linearized graphs.
       Answer all of the questions on this activity sheet.




[I can’t drive 55!]                                                                              [Page 5 of 5]

								
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