Olympic Dreams Coming True - The Problems
08/23/2004

 

Last week American Paul Hamm became the first American to win the Men’s Gymnastics All-Around gold medal, and he did it in amazing style. After a terrible result in his fourth event (vault), he was in 12th place with just two events remaining. He ended up winning the all-around title by just .012 points over Kim Dae Eun of South Korea who finished the competition with 57.811 points. If Hamm averaged 9.837 points on each of his last two events, what was his point total after the disastrous fourth event?

Though Hamm may have become the American hero of the Olympics with his amazing victory, all eyes are still on American swimmer Michael Phelps. Though we know (even at the time of writing this problem) that he will not earn eight gold medals, he is still on track to win eight Olympic medals. If we had been told before the Olympics started that Phelps would win eight medals, and he would win at least as many gold medals as bronze medals, how many different medal-combinations would satisfy these requirements?

One lap (back and forth) of the Olympic pool is 100 meters, and Phelps averaged 59.26 seconds to swim this distance in one of his victories. How many minutes would it take him to complete a 1-mile swim if he averages 59.26 seconds per 100 meters throughout the swim? Express your answer to the nearest whole number. (Use 1 km = 0.62137 miles)

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December 27, 2004
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