ARE WE THERE YET?
Stephanie and Linda are close friends, and they want to meet up to play. Although the girls live on the
same street, their houses are 240 yards apart. Neither girl wants to walk the full distance, so they
decide to leave home, at the same time, and meet somewhere in the middle.
The following equations represent the distance (d), in yards, between each girl and Stephanie’s house,
as a function of time (t), in minutes.
Equation 1: d= 20t
Equation 2: d= -40t + 240
1. Graph each equation. (Be sure to label your graphs.)
2. Which girls travel is modeled by Equation 1? __Stephanie_ Equation 2? ___Linda_____
Explain.____Since d represents the distance from Stephanie’s house, the equation with a y-intercept of
zero is the one that model’s Stephanie’s position, and the equation with a y-intercept of 240 is the one
that model’s Linda’s position._________________________________________________________
3. . In words, explain what the -40 in Equation 2 represents?_As,time passes, Linda is getting closer to
Stephanie’s house. The distance is decreasing.__________________________________
4. Which girl is walking faster?__Linda___ Explain. ___Slope represents the yards per minute, which is
speed. Stephanie is walking at 20 yards per minute and Linda is walking at 40 yards per minute._______
5. What ordered pair would you use to describe Stephanie’s original position? ____(0,0)_________
6. When will the girls meet? ___After four minutes.__________
7. How far will they be from Stephanie’s house? _____80 yards______
The following graphs represent the distance (d), in yards, between each girl and Linda’s house, as a
function of time (t), in minutes.
8. Write an equation for Line A. _______d = 40t__________________
9. Which girl’s travel is modeled by the equation in #8? ____Linda____
Explain. _We know that Linda is walking at a speed of 40 yards per minute (slope=40), and she starts at
her own house (y-intercept = 0).________________________________________________________
10. Write an equation for Line B. _______d = -20t + 240_______________
11. Which girl’s travel is modeled by the equation in #8? _________Stephanie___________________
Explain. __We know Stephanie is walking at a speed of 20 yards per minute and getting closer to
Linda’s house (slope = -20), and we know that she starts at a distance of 240 yards away from Linda’s
house (y-intercept = 240)._____________________________________________________
12. How long would it take for Stephanie to walk from her house to Linda’s house? __12 minutes__
Explain. __Answers may vary. Some examples are: Solve equation 1 when d = 240. Find the
horizontal-intercept of Line B (distance to Linda’s house is 0.__________________________________
13. How long would it take for Linda to walk from her house to Stephanie’s house? __6 minutes_____
Explain. ___Answers may vary. Some examples are: Solve equation 1 when d=0. Find the t-coordinate
for Line A, when d=240. _________________________