Question

Al Unser won the Indianapolis 500-mile race in 1987. Juan Pablo Montoya won the Indianapolis 500-mile race in 2015. Unser completed his race in 3.083089 hours. Montoya completed his race in 3.099033 hours. Imagine that they drove their exact races against each other and that the race ended when the winner crossed the finish line. This question concerns the imaginary race.

Recall that, in the Unser-Montoya Intro Problem, you created the following definitions: for all 0≤t≤3.0830890≤t≤3.083089, n(t) is the number of miles Montoya has traveled t hours after the race began, and m(t) is the number of miles Unser has traveled tt hours after the race began.

(a) Represent those times when Unser was ahead of Montoya.

All 0≤t≤3.083089 such that

(b) Explain how what you wrote for part (a) represents what you claim.

(c)Represent the moment(s) in time when Unser was exactly 0.23 miles ahead of Montoya.

All 0≤t≤3.083089such that    

(d) Explain how what you wrote for part (c) represents what you claim.

(e) Is it possible that your answer for part (c) has more than one solution? Why or why not?

• No, because Unser is always ahead of Montoya
• Yes, because Unser might be .23 miles ahead at different times
• No, because Unser is only .23 miles ahead of Montoya once because two linear graphs only intersect once
• Yes, because Unser is always ahead of Montoya

Answer 1

(a)

(b) Unser runs for 3.083089 hours. Thus t must be less than or equal to 3.083089.

Also, Unser is ahead of Montoya if at any time t,

(c)

(d) Unser runs for 3.083089 hours. Thus t must be less than or equal to 3.083089.

Also, Unser is exactly 0.23 miles ahead of Montoya if at time t,

(e) No, because Unser is only 0.23 miles ahead of Montoya once because two linear graphs only intersect once.