Two Graphing Stories
Name: __________________________________ Date: ________________
Directions: Use the following information to answer problems 1 through 5.
Maya and Earl live at opposite ends of the
hallway in their apartment building. Their
doors are 50 feet apart. They each start at
their door and walk at a steady pace towards
each other and stop when they meet. Suppose
that Maya walks at a constant rate of 3 feet
every second and that Earl walks at a constant
rate of 4 feet every second.
1. Graph both people’s distance from Maya’s
door versus time in seconds.
2. According to your graphs, approximately
how far will they be from Maya’s door when
they meet?
3. Write the equation for Maya’s line.
4. Write the equation for Earl’s line.
5. Use the substitution method to find out exactly how much time it took for Maya
and Earl to meet in the hallway and to find out the exact distance.
Directions: Use the following information to answer problems 6 through 9.
May, June and July were running at the track. May started first and ran at a
steady pace of 1 mile every 11 minutes. June started 5 minutes later than May and
ran at a steady pace of 1 mile every 9 minutes. July started 2 minutes after June
and ran at a steady pace, running the first lap (1/4 of a mile) in 1.5 minutes. She
maintained this steady pace for 3 more laps and then slowed down to 1 lap every 3
minutes.
6. Sketch May, June and July’s distance versus time graphs on a coordinate plane.
7. Who is the first person to run 3 miles?
8. Did June and July pass May on the track? If they did, when and at what
mileage?
9. Did July pass June on the track? If she did, when and at what mileage?
Directions: Use the following information to answer problems 10 through 14.
Suppose two cars are traveling north along a road. Car 1 travels at a constant speed of 50 mph for
two hours, then speeds up and drives at a constant speed of 100 mph for the next hour. The car
breaks down and the driver has to stop and work on it for two hours. When he gets it running again,
he continues driving recklessly at a constant speed of 100 mph. Car 2 starts at the same time as
Car 1 starts, but Car 2 starts 100 miles farther north than Car 1. Car 2 travels at a constant speed
of 25 mph throughout the trip.
10. Sketch the distance versus time
graphs for Car 1 and Car 2 on a coordinate
plan. Start with time 0 and measure time
in hours.
11. Approximately when do the cars pass
each other?
12. Tell the entire story of the graph from the point of view of Car 2. (What does
the driver of Car 2 see along the way and when?)
13. Write a linear equation for Car 2.
14. Suppose that Car 1 travels at the constant speed of 25 mph the entire time.
Do the cars pass each other? Write the equation of the line for Car 1 in this
situation.
Directions: Use the following information to answer questions 15 through 20.
The following graph shows
the revenue (or income) a
company makes from designer
coffee mugs and the total
cost (including overhead,
maintenance of machines,
etc.) that the company spends
to make the coffee mug.
15. How are revenue and
total cost related to the
number of units of coffee
mugs produced?
16. What is the meaning of the point (0, 4000) on the total cost line?
17. What are the coordinates of the intersection point? What is the meaning of
this point in this situation?
18. Write a linear equation for the Total Cost.
19. Write a linear equation for the Revenue.
20. The company makes a profit when the Revenue exceeds the Total Cost. What
will the profit be if the company makes and sells 1,000 mugs?