Is the division from the previous problem envy-free? Explain.
Reference:
Consider the team triathlon information from problem 7.
a. If the race is divided into the following options, who must have been the divider? Explain how you know.
Option I: 6-mile run, 27-mile bike ride, 1-mile swim
Option II: 4-mile run, 26-mile bike ride, 7-mile swim
Option III: 6-mile run, 27-mile bike ride, 1-mile swim
b. Determine the result of applying the divide-and choose method.
Problem 7:
A team triathlon consists of a 16-mile run, an 80-mile bike ride, and a 9-mile swim. A team consists of three members. Matt’s running-to-biking-to-swimming preference ratio is 1 to 4 to 1, Jory’s ratio is 2 to 2 to 1, and Sart’s ratio is 3 to 1 to 4. The events will be divided according to the divide-and-choose method for three players.
a. How would each teammate value the entire race, and what would be a fair share according to each person?
b. Would a 3-mile run, a 19-mile ride, and a 4-mile swim be considered a fair share by any of the three teammates? Justify your answer.
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