Three friends, Alice, Bob, and Carlos, want to have a race on their electric scooters. Aware...

   

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Three friends, Alice, Bob, and Carlos, want to have a race on their electric scooters. Aware that he is the fastest rider, Bob claims he can ride nlog2(n) miles faster than Alice can ride n miles and Carlos can ride log2 n miles, for any value of n. Suppose Bob's speed is 30 miles per hour, Alice's speed is 15 miles per hour, and Carlos's speed is 6 miles per hour. We will show that Bob is incorrect (he has never taken a Discrete Structures course, evidently!). (a) [4 pts.] How large must n be to ensure that Alice finishes before Bob? Justify your answer. (b) [4 pts.] How large must n be to ensure that Carlos finishes before Bob? Justify your answer. (c) [4 pts.] As n gets increasingly large, who completes their ride first, Alice or Carlos? Justify your answer. Three friends, Alice, Bob, and Carlos, want to have a race on their electric scooters. Aware that he is the fastest rider, Bob claims he can ride nlog2(n) miles faster than Alice can ride n miles and Carlos can ride log2 n miles, for any value of n. Suppose Bob's speed is 30 miles per hour, Alice's speed is 15 miles per hour, and Carlos's speed is 6 miles per hour. We will show that Bob is incorrect (he has never taken a Discrete Structures course, evidently!). (a) [4 pts.] How large must n be to ensure that Alice finishes before Bob? Justify your answer. (b) [4 pts.] How large must n be to ensure that Carlos finishes before Bob? Justify your answer. (c) [4 pts.] As n gets increasingly large, who completes their ride first, Alice or Carlos? Justify your answer.