SCMP November 2009
THE BIG RACE
One of the annual events at school during Spirit Week is a tricycle race held in the gym. Leslie has won the race each of the last three years and is starting to brag about it. The rest of the class is annoyed by this attitude and wants to end this winning streak. Since you will also compete, you need to size up the competition.
Leslie rides at a constant rate of 2 meters per second. On neatly scaled axes, graph a line to represent her position and label the line with her name and an equation in terms of x and y that shows the distance Leslie travels. Let x represent time in seconds and y represent the distance in meters. We do not know how long the race will be, so extend your graph appropriately.
Dina wants to see if she can win the Big Race with a 3 meter head start. If she can ride her tricycle 1 meter per second, can she beat Leslie? Using her speed and her head start, graph a line for Dina on the same set of axes. Label her graph with her name and equation. Be sure to extend her line as far as possible. Use different colors to help keep each competitor identified.
Ms. Speedi, the teacher, is planning on starting at the finish line and walking toward the starting line when the race starts. If she walks one meter per second and meets Dina 11 seconds after the start of the race, how long is the race? Graph Ms. Speedi’s distance from the starting line on the graph. Label this line with the teacher’s name and an equation.
Dean has decided he will enter the race. He estimates that he rides 3 meters every 4 seconds and wants a 2 meter head start. On the same set of axes, graph a line representing Dean’s distance from the starting line. Label his line with his name and equation.
Elizabeth and Bob are considering joining the race. Bob usually rides 3 meters in 2 seconds and will get a 5 meter head start. Elizabeth rides 1 meter in 4 seconds and wants a 6 meter head start. Add lines for them and label each line with the equation and person’s name. Who rides faster, Elizabeth or Bob? How does the graph show this? When does Dean pass Elizabeth? How can you tell by examining the graph?
If Brian starts 3 seconds late and catches up with Dina 7 seconds after the race begins, add Brian’s line to the graph. What is the x-intercept for Brian’s line? Find his speed. What is his equation? Label his line with his name and equation.
Who is going to win the race based on the information you have been given? Write a summary of the results listing the order in which the participants would finish the race. How do the different speeds and starting positions of each participant affect their equations? How did you determine the length of the race?
Adapted from College Preparatory Mathematics, Mathematics 1, Second Edition, 2000
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