Women Finish First (Men Still Run Faster) - The Solutions
04/26/2004

First, we need to determine how much faster the winning man ran the race. Subtracting the times we see this difference is13 minutes, 50 seconds. However, because the woman started 29 minutes ahead of the man, we must subtract this time from 29 minutes and we get 15 minutes, 10 seconds.

The difference between the first and thirteenth times is 15 minutes, 8 seconds. This is equivalent to 908 seconds. If the first 13 times form an arithmetic sequence, then the common difference was added to the winner’s time a total of 12 times to get to the thirteenth place time. Dividing 908 by 12 gives us 75 and 2/3 seconds between each of the 13 consecutive male finishers. The tenth place finisher would then have a time of 2 hours, 10 minutes, 37 seconds + 9(75.6666667) seconds = 2 hours, 10 minutes, 37 seconds + 11 minutes,21 seconds = 2 hours, 21 minutes, 58 seconds.

Since there were 80 pounds at each of 26 stops, that’s 80 × 26 = 2080 pounds! A ton is equivalent to 2000 pounds, so we see that the ice weighs more than 100% of a ton. Performing 2080 ÷ 2000, we see that it is actually 104% of one ton.