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Home > AC > Chapter 7 > Lesson 7.2.2 > Problem 7-65



Barbara, Elizabeth, and Carlos participated in the second heat of “The Big Race.” Barbara thought she could win with a head start even though she only pedaled meters every seconds. Elizabeth began at the starting line and finished the race in seconds. Meanwhile, Carlos rode his tricycle so that his distance from the starting line in meters could be represented by the rule , where represents time in seconds.  

  1. Using the given information, graph lines for Barbara, Elizabeth, and Carlos on the same set of axes. Who won the race and will advance to the final race?

  2. Find rules that describe Barbara's and Elizabeth's motion.

    What are the slope and y-intercept of each of their lines?

  3. How fast did Carlos pedal?

    Use the graph. What part of the graph shows his rate? How far does Carlos pedal each second?

  4. When did Carlos pass Barbara? Confirm your answer algebraically.

    After 2 seconds. Where is this shown on the graph? Use the Equal Values Method to confirm your answer algebraically.

Use the points in the eTool to graph each person's starting point and progress.
Click the link at right for the full version of the eTool: AC 7-65 HW eTool