Alice, Bob, and Cindy each drive about 1000 miles per month. Alice drives a truck which gets 10 mpg. Bob drives a 20 mpg car. Cindy drives a smaller vehicle which averages 40 mpg. The goal is to find the 3 friend's "average" mpg... Computing the regular arithmetic mean of the 3 mpg will lead to an incorrect average. Instead, there are two alternatives. One, invert each mpg to get gpm then compute the arithmetic mean, then re-invert back to mpg [this method is called a Harmonic Mean). Two, find the total number of miles driven and the total number of gallons used, then divide. Execute one or both of these methods and compare/contrast to the incorrect arithmetic mean. The three friends plan to buy newer, more efficient vehicles. Alice's new truck will get 13mpg. Bob is upgrading to a 28mpg car. Cindy is looking at a 55mpg hybrid. Who will save more gasoline with these upgrades? What upgraded mpg would the other two have needed in order to save the same amount? Again, there are two ways to find the answers. One, compare the gpm for each person's new car to their old car. Then find out how many gpm are saved by each person. Finally, take the largest saved gpm and apply that savings to the other two before inverting back. Two, compare the gallons used for each person's new car to their old car (each month). Then take the largest saved number of gallons and apply to the other two. Execute one or both of these methods and summarize!