Your submission must be turned in on canvas by 5pm on Friday, Feb 22, 2019. This project is worth 20 points (4% of your final grade) in the calculation of your final grade. One point (0.2% of your final grade) is deducted for every 6 hours the project is late.
This page will give you the context of the problem that you will analyze, then six prompts for your response, and finally a rubric describing how your responses will be evaluated.
Harriet and Tori are running a series of half-marathons. During the first one, Harriet ran at about 7.5 mph for an hour, but then took a 45 minute nap. Feeling completely rested, she continued at 7.5 mph until the race was done: another 45 minutes. Her finish time was recorded at 2 hours, 29 minutes, and 48 seconds. Tori ran the same half-marathon, but kept a steady 6.5 mph pace until the race was done. Her time was recorded at 2 hours and 55 seconds.
Harriet and Tori receive a lot of advice from people who did not run the race.
Uncle Robert, Harriet's uncle, speaks at length about the importance of interval training and how 45 minutes is much too long for a nap. Robert's rule is that you should take three 15 minute naps instead: run for 30 minutes, nap for 15, run for 30, nap for 15, run for 30, nap for 15, and then run the rest until you are done.
How much would Harriet's time have been improved if she used Robert's rule? How much help is Robert's advice?
Aunt Issa told Harriet that she took her nap much too late in the race. 30 minutes into the race, that's when you take a nap. 45 minutes is a good nap, but Harriet needed to take it after the first half hour, not after the first hour.
How much would Harriet's time have been improved if she had taken Issa's advice?
Graph the four possible runs: Harriet's actual run, Robert's rule for Harriet, Issa's advice for Harriet, and Tori's run. Have the horizontal axis be time, and the vertical axis be how far the runner has gone total so far.
Compute the average rate of change (or average speed) of the four possible runs, and indicate how they are related to the graphs.
Find an authoritative source for the average half-marathon pace. How do each of the four times compare?
What is wrong with the following calculation:
Harriet ran 7.5 mph when she ran, but when she napped it was 0 mph. That means her average speed was (7.5+0)/2 = 3.75 mph. That's why it took Harriet so much longer than Tori.
How long would a runner whose average speed was 3.75 mph take to do a half-marathon?
What is wrong the following calculation:
Harriet ran 7.5 mph when she ran, but when she napped it was 0 mph. However, she ran, then napped, then ran. That means her average speed was (7.5+0+7.5)/3 = 5 mph. That's why it took Harriet so much longer than Tori.
How long would a runner whose average speed was 5 mph take to do a half-marathon?
Why doesn't the "average" in those calculations work?
How would you explain to how to correctly compute the average speed? Make sure it would help someone evaluate Robert's and Issa's advice very quickly. Indicate how it relates to the graphs, and how it relates to the nap.
Your submission must be turned in on canvas by 5pm on Friday, February 22, 2019. This project is worth 20 points (4% of your final grade) in the calculation of your final grade. One point (0.2% of your final grade) is deducted for every 6 hours the project is late.
Your response to #1 and #2 will be graded on the clarity of your critique and its mathematical correctness. It should clearly identify the issues with the advice. Just numbers or equations will receive very little credit.
Your response to #3 will be graded on the clarity of your graph and the correctness of your calculations. Make sure you indicate how everything is related. Your response to #4 will be graded on the appropriateness and authority of your source and how well it relates to Harriet's and Tori's reported times.
Your response to #5 and #6 will be graded on the clarity of your analysis and its mathematical correctness. Not only do you need to calculate some numbers, you need to indicate how and why some of those numbers are wrong. For #6, you'll need to give a mathematical formula for the correct answer in terms of the nap. The answer to #6 is definitely not a single number.