### Home > CCA > Chapter 2 > Lesson 2.2.2 > Problem 2-61

Barbara, Mark, and Carlos participated in the third heat of “The Big Race.” Barbara thought she could win with a ) from the starting line in meters could be represented by the equation

*, where*

*represents time in seconds.*

*2-61 HW eTool*(Desmos). Homework Help ✎

What is the dependent variable? What is the independent variable?

Between time and distance in this race, which variable changes? Which stays the same?

Using the given information, graph lines for Barbara, Mark, and Carlos on the same set of axes. Who won the

meter race and will advance to the final race? Every

seconds, Barbara will go up meters. At seconds, Mark will be done with the meters. Use these clues as well as the equation given for Carlos to make a graph. Find equations that describe Barbara’s and Mark’s motion.

The slope is the distance over the time (given) and the

-intercept is where they were when the race began, at seconds. (Remember Barbara had a head start). How fast did Carlos pedal? Write your answer as a unit rate.

If the slope is distance over time, what does the slope in the given equation tell us about Carlos' speed?

meters every seconds

Now write this as a unit rate.When did Carlos pass Barbara? Confirm your answer algebraically.

On the graph, at what point does Carlos' line cross Barbara's line? To confirm it algebraically, set the two equations equal to each other and solve for time

.

Complete the tables in the eTool below to graph the results and solve the parts.

Click the link at right for the full version of the eTool: *CCA 2-61 HW eTool*