Team 6285 HiMCM 2016 Page 1 of 19 Problem A Paper: Swim, Bike, and Run The mayor of a town wants to support a local youth group by hosting a triathlon. Participants must swim 1500 m, bike 40 km, and run 10 km. Racers must transition between each stage. There will be a wide variety of skill levels, ranging from professional to amateur. About 2000 contestants are expected to attend, but a small buffer of five percent was added to the expected attendance for safe measure. Several triathlons have divisions for the athletes based on gender, age, and skill level. People will compete against other runners in their division but will not always run with them. These divisions will yield multiple winners from the 2000 expected participants. Additionally, the mayor wants to minimize the course congestion and the time spent on the roads because the roads can only be closed for five and a half hours. The team was tasked with making a triathlon by examining collections of data from previous triathlons. The team found that the participant count per wave is 50 people. The average time interval in between waves of contestants will be three minutes. Using this information, the team constructed 43 waves consisting of mixed genders, ages, and experience, but common previous final times. The wave of the slowest contestants would begin and after a three minute intervals the next wave of people would begin. Both a scatter plot and a box and whisker plot were constructed which suggest that there will be no major clogging of the streets. The team was also told to find advantages in changing the distances of the triathlon. An equation that defined velocity as a function as time was used to account for decreases in stamina. The results indicate that the best possible solution for minimizing the road closure time and course congestion is to shorten the distances of cycling and running and leave the swimming section constant.
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Team 6285 HiMCM 2016 Page 1 of 19
Problem A Paper: Swim, Bike, and Run
The mayor of a town wants to support a local youth group by hosting a triathlon.
Participants must swim 1500 m, bike 40 km, and run 10 km. Racers must transition between
each stage. There will be a wide variety of skill levels, ranging from professional to amateur.
About 2000 contestants are expected to attend, but a small buffer of five percent was added to
the expected attendance for safe measure. Several triathlons have divisions for the athletes based
on gender, age, and skill level. People will compete against other runners in their division but
will not always run with them. These divisions will yield multiple winners from the 2000
expected participants. Additionally, the mayor wants to minimize the course congestion and the
time spent on the roads because the roads can only be closed for five and a half hours. The team
was tasked with making a triathlon by examining collections of data from previous triathlons.
The team found that the participant count per wave is 50 people. The average time interval in
between waves of contestants will be three minutes. Using this information, the team constructed
43 waves consisting of mixed genders, ages, and experience, but common previous final times.
The wave of the slowest contestants would begin and after a three minute intervals the next wave
of people would begin. Both a scatter plot and a box and whisker plot were constructed which
suggest that there will be no major clogging of the streets. The team was also told to find
advantages in changing the distances of the triathlon. An equation that defined velocity as a
function as time was used to account for decreases in stamina. The results indicate that the best
possible solution for minimizing the road closure time and course congestion is to shorten the
distances of cycling and running and leave the swimming section constant.
Team 6285 HiMCM 2016 Page 2 of 19
Dear Mayor Lawrence,
The triathlon that you requested will be a great success! As of now, we are expecting
approximately 2000 participants, but there is a possibility that more people may attend than
expected. Therefore, the triathlon has been designed to accommodate a five percent increase in
the number of expected athletes, allowing for an additional 100 competitors. To establish a
competition between the participants, divisions of contestants have been devised based on
gender, age, and skill level. Participants have also been divided into separate waves indicating
starting times. Participants will compete with people in only the same division, not necessarily
the same wave. In order to minimize course congestion, the participants were divided into 43
separate waves based on their final time results from a previous triathlon. The first wave will
start the course at 12:00 p.m. and will be followed by a new wave every three minutes.
Moreover, the time delay will lower the amount of course congestion by allowing leading
athletes to distance themselves from succeeding groups. Creating distance between participants
will effectively make the course safer by preventing collisions. If the roads are closed to the
public by 12:28 p.m., then the town can reopen local roads exactly five hours and thirty minutes
after the roads were blocked off. Before 12:28 p.m., the expected participants will not have
reached the cycling stage yet; the participants will not have completed transition one and
therefore, the roads may remain open to the public. At 5:58 p.m., the roads should be once again
opened to the public. Ultimately, the decreasing of congestion and the ability to reopen roads in
minimal time will lead to a successful event. The corresponding schedule is attached.
Best Regards
(The Schedule is attached at the end of the appendix)
Team 6285 HiMCM 2016 Page 3 of 19 Triathlon Day Schedule