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Math in the News: Issue 95

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In this issue of Math in the News we look at the Iditarod Race in Alaska. This gives us an opportunity to analyze data on average speed. We look at data in tables and line graphs and analyze the winning speeds over the history of the race.

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Math in the News: Issue 95

1. 1. The Iditarod Race Math in the News Issue 95
2. 2. The Iditarod Race This year’s Iditarod happens during a particularly harsh winter. This 1000-mile race is an endurance competition for musher and dog alike. In this issue we measure the average speed of the racers.
3. 3. The Iditarod Race The Iditarod Race began in 1973, in part to commemorate a heroic Anchorage-to-Nome delivery of diphtheria serum that made a husky by the name of Balto famous to children the world over. It is now a world-wide sporting event.
4. 4. The Iditarod Race This is the map of this year’s Iditarod Race. This is the Northern route. On odd-numbered years there is a Southern route. As you can see this 975-mile route is not a straight-line distance from Anchorage to Nome.
5. 5. The Iditarod Race This table shows the winning times for the all the racers since the first Iditarod. The first thing to notice is that these times have steadily increased, as mushers have improved their speeds over time. (Table continued on the next slide.) Source: Iditarod.com Year Days Hours Minutes Seconds 1973 20 0 49 41 1974 20 15 1 7 1975 14 14 43 15 1976 18 22 58 17 1977 16 16 27 13 1978 14 18 52 24 1979 15 10 37 47 1980 14 7 11 51 1981 12 8 45 2 1982 16 4 40 10 1983 12 14 10 44 1984 12 15 7 33 1985 18 0 20 17 1986 11 15 6 0 1987 11 2 5 13 1988 11 11 41 40 1989 11 5 24 34 1990 11 1 53 23 1991 12 16 34 39
6. 6. The Iditarod Race Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Days 10 10 10 9 9 9 9 9 9 9 8 9 9 9 9 9 9 9 9 9 9 Hours 19 15 13 2 5 8 5 14 0 19 22 15 12 18 11 5 11 21 23 18 4 Minutes 17 38 2 42 43 30 52 31 58 55 46 47 20 39 11 8 46 38 59 46 29 Seconds 15 15 39 19 0 45 26 7 6 50 2 36 22 31 36 41 48 46 9 39 26
7. 7. The Iditarod Race Take the data in the table and input it into a spreadsheet. Create a new column to convert the times to hours. Year 1973 1974 1975 1976 1977 1978 1979 1980 Days 20 20 14 18 16 14 15 14 Hours 0 15 14 22 16 18 10 7 Minutes Seconds Hours 49 41 480.83 1 7 495.02 43 15 350.72 58 17 454.97 27 13 400.45 52 24 354.87 37 47 370.63 11 51 343.20 =B2*24+C2+D2/60 +E2/3600
8. 8. The Iditarod Race Create a line graph of the data for the winning times. Here you can see how the winning times have steadily decreased, and now hover around 200 hours.
9. 9. The Iditarod Race Now add another column to the spreadsheet to calculate the average speed. Year 1973 1974 1975 1976 1977 1978 1979 1980 Hours 480.83 495.02 350.72 454.97 400.45 354.87 370.63 343.20 Average Speed (mi/h) 2.028 1.970 2.780 2.143 2.435 2.747 2.631 2.841 =975/F2
10. 10. The Iditarod Race Here is a line graph of the speed data, and it clearly shows a steady improvement in the average speed.
11. 11. The Iditarod Race Why have the times increased so steadily?
12. 12. The Iditarod Race First, let’s refine our speed estimate. The average speed we calculated assumes the mushers are riding 24/7, which isn’t true. There’s a mandatory 40-hours of rest minimum. Adjust your spreadsheet to see the impact on the speeds. Year 1973 1974 1975 1976 1977 1978 1979 1980 Hours 480.83 495.02 350.72 454.97 400.45 354.87 370.63 343.20 Average Speed (mi/h) 2.028 1.970 2.780 2.143 2.435 2.747 2.631 2.841 Reduce by 40
13. 13. The Iditarod Race Here is a double line graph of the speed data sets, and it clearly shows an increase in the average speed.
14. 14. The Iditarod Race Now assume that of the remaining hours, a musher spends between 15% to 20% of their time resting. (People normally spend 33 1/3% resting.) How does this affect the speed? Here is a multi-line graph showing such an adjustment.
15. 15. The Iditarod Race • Continue investigating ways in which racers have increased their average speed. Keep these questions in mind: • • • Do racers maintain the same speed throughout the entire race? If not, how does their speed vary? How does the number of dogs used in the race affect the average speed? What techniques do racers use to improve their speed?