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 Car1 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?