Cook, Cameron

Lenhart, Suzanne

Wiggins, Gregory J

English

University of Tennessee, Knoxville: Trace

University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Educational Resources National Institute for Mathematical and Biological Synthesis (NIMBioS) 2021 Modeling an Ironman Race (High School) Cameron Cook National Institute for Mathematical and Biological Synthesis (NIMBioS) Gregory J. Wiggins National Institute for Mathematical and Biological Synthesis (NIMBioS) Suzanne Lenhart National Institute for Mathematical and Biological Synthesis (NIMBioS) Follow this and additional works at: https://trace.tennessee.edu/utk_nimbiosed Recommended Citation Cook, C., Wiggins, G., Lenhart, S. (2021). Modeling an Ironman Race. National Institute for Mathematical and Biological Synthesis (NIMBioS), QUBES Educational Resources. https://www.doi.org/10.25334/TX6Y-ZN14 This Creative Written Work is brought to you for free and open access by the National Institute for Mathematical and Biological Synthesis (NIMBioS) at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Educational Resources by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact trace@utk.edu. Modeling an Ironman RaceJune 30, 2018A triathlon is a 3 sport event consisting of swimming, biking, and running (in that order). Triathlonscan be of various lengths. The longest distance being that of the Ironman distance triathlon. This racetotals in 140.6 total miles. The breakdown is as follows; 2.4 miles swimming, 112 miles biking, and26.2 miles running. Simon is preparing to do his first Ironman triathlon and wants to have a realisticidea of how his race might go. Create a model that represents a realistic Ironman race.1. What assumptions are you making?2. What are your variables?3. Write your model.4. Tell about your results.1Uses Algebra 1 concepts5. Graph your results6. How could you have modeled the Ironman race in a different way?Prepared by Cameron Cook, Suzanne Lenhart and Greg Wiggins for NIMBioS2Modeling an Ironman Race KeyJune 30th 2018A triathlon is a 3 sport event consisting of swimming, biking, and running (in that order). Triathlonscan be of various lengths. The longest distance being that of the Ironman distance triathlon. This racetotals in 140.6 total miles. The breakdown is as follows; 2.4 miles swimming, 112 miles biking, and26.2 miles running. Simon is preparing to do his first Ironman triathlon and wants to have a realisticidea of how his race might go. Create a model that represents a realistic Ironman race.1. What assumptions are you making?I will assume Simon swims 2mph for the entirety of the swim component, bikes 16mph for theentirety of the bike component, and runs 7mph for the entirety of the run component. I will alsoassume that he instantly begins each new piece of the race(i.e. takes no time to transition fromone piece to another)2. What are your variables?Time t is the amount of time elapsed (since the beginning of the race) when the competitorhas completed a distance d in miles. You could model this situation a number of ways. Note itis not often time is the dependent variable in models, but in this case it makes since to considerthis as your race time depends on how fast you travel a certain distance.3. Write your model.t(d) =d20 ≤ d ≤ 2.41.2 + d−2.4162.4 < d ≤ 114.48.2 + d−114.47114.4 < d ≤ 140.614. Tell about your results.The total time is 11.94 hours. The first piece was the simplest to determine since we were start-ing from time 0. Time= Distance/Velocity, so the time during that component is determined bydistance/2. Now, for the next two piece if we want our function to model the accumulated timefor the whole race we need to start the second leg, the bike, at the time the swim leg ended, thusthe 1.2 hour shift. We also want to consider the triathlon as an accumulation of the three events.Thus, we want the bike event to start at mile 2.4 and we show that mathematically with theindependent variable shift before dividing the distance by the velocity to obtain the time spentcompleting that component. The running piece was calculated similarly to the biking piece. Also,note that the slope is not the speed. So a larger slope does not mean a higher speed.5. Graph your results20 40 60 80 100 120 140246810dt6. How could you have modeled the Ironman race in a different way?One could consider each piece separately. One could also model distance as a function of time(Probably a more common way to do this), or velocity or model time as a function of velocity.Or, one could model velocity as a function of time or distance. Distance vs time is nice as theslope would be the speed of the athlete in each piece, the times spent in each event would needto be found in order to write the piecewise function.Prepared by Cameron Cook, Suzanne Lenhart and Greg Wiggins for NIMBioS2

Modeling an Ironman Race (High School)

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Modeling an Ironman Race (High School)

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University of Tennessee, Knoxville: Trace