THE BIG RACE − HEAT 2

Barbara, Elizabeth, and Carlos participated in the second heat of “The Big Race.” Barbara thought she could win with a $3\text{-meter}$ head start even though she only pedaled $3$ meters every $2$ seconds. Elizabeth began at the starting line and finished the $20\text{-meter}$ race in $5$ seconds. Meanwhile, Carlos rode his tricycle so that his distance $\left(y\right)$ from the starting line in meters could be represented by the rule $y=\frac{5}{2}x+1$, where $x$ 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 $20\text{-meter}$ race and will advance to the final race?

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

   Hint (b):

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

3. How fast did Carlos pedal?

   Hint (c):

   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.

   Answer (d):

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