Maxine prefers biking to running in a ratio of 5 to 2. Mary prefers biking to running in a ratio of 1 to 3. Together, they will participate in a team competition consisting of a 70-mile bike ride and a 6-mile run. It is up to the teams to divide the biking and running portions of the event however they want. Use points to assess value.
a. How many points would Maxine assign to the entire competition?
b. Would 31 miles of biking and a 1-mile run be a fair share according to Maxine’s values? Explain.
c. Suppose Maxine divides the race into the following two options:
Option I: 4-mile run and 34.6-mile bike ride
Option II: 2-mile run and 35.4-mile bike ride
What value would Mary place on each option, and which would she choose?
d. Describe a fair division by Mary that includes 29 miles of biking. Explain which option Maxine would choose and why.
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