Question: Al Unser won the Indianapolis 500-mile race in 1987. Tony Canaan won the Indianapolis 500-mile race in 2013. Unser completed his race in 3.083089 hours. Canaan completed his race in 2.667616 hours. Imagine that they drove these races against each other and that the race ended when the winner crossed the finish line. Let t represent the number of hours since their imaginary race started.
1) Use function notation to represent the distance that each driver traveled in relation to the number of hours since the race began. Be sure to state what every letter you use represents. State the domain of your independent variable.
2) Represent each of the following using function notation. Explain how what you wrote represents what you claim: a) the distance that Unser traveled in its first 0.09 hours of the race. b) the distance that Canaan traveled in the first 97 minutes of the race c) the distance that Unser traveled from t=1.192 to t=2.013 hours. d) the distance that Canaan traveled in any one-minute time period.
3) Represent the distance between Unser and Canaan at the end of the race. Explain how what you wrote represents what you claim.
4) Represent the distance between Canaan and Unser at ever moment from when the race began to when it ended.
5) Represent those times when Unser was ahead of Canaan.
6) Represent the fact that Canaan was ahead of Unser when Canaan finished the race.
7) Represent the moments in time when Canaan was 0.23 miles ahead of Unser. Why is it possible that your equation can have more than one solution?