Answer :
To determine which scenarios are true based on the elevation data provided for Melissa and Corey, let's analyze each scenario one-by-one using the given information from the table:
| Time (min) | Melissa's Elevation (feet) | Corey's Elevation (feet) |
|------------|-----------------------------|---------------------------|
| 0 | 8,342 | 10,004 |
| 30 | 9,550 | 11,432 |
| 60 | 11,239 | 12,921 |
| 90 | 12,921 | 11,075 |
| 120 | 12,921 | 10,004 |
1. Melissa and Corey started on different trails:
To check if they started on different trails, we compare their elevations at time 0 minutes:
- Melissa: 8342 feet
- Corey: 10004 feet
Since their elevations at the start are different, it is clear that they started on different trails.
Conclusion: This scenario is true.
2. Melissa hiked up the trail for a longer period of time than Corey:
To determine who hiked up the trail for a longer period, we need to find the duration for which their elevation was continuously increasing:
- Melissa's elevation increased from 0 to 90 minutes.
- Corey's elevation increased from 0 to 60 minutes, and then began to descend from 60 minutes to 120 minutes.
Therefore, Melissa hiked upward for the entire 90 minutes, while Corey hiked upward only for 60 minutes before descending.
Conclusion: This scenario is true.
3. Melissa and Corey crossed paths between 60 and 90 minutes:
To check if they crossed paths, we need to see if they had the same elevation at any time between 60 and 90 minutes:
- At 60 minutes: Melissa - 11,239 feet, Corey - 12,921 feet
- At 90 minutes: Melissa - 12,921 feet, Corey - 11,075 feet
Clearly, their elevations are never the same between 60 and 90 minutes.
Conclusion: This scenario is false.
4. Corey began his descent before Melissa:
To determine who began their descent first, we look at when each hiker's elevation started to decrease:
- Corey: His elevation starts to decrease after 60 minutes (it was highest at 60 minutes and then lower at 90 minutes).
- Melissa: Her elevation did not decrease; it stayed constant from 90 to 120 minutes.
Since Corey’s elevation started descending after 60 minutes and Melissa’s did not descend at any point, Corey began his descent before Melissa.
Conclusion: This scenario is true.
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased:
We need to check Melissa’s elevation from 0 to 60 minutes:
- At 0 minutes: 8342 feet
- At 30 minutes: 9550 feet
- At 60 minutes: 11239 feet
Melissa's elevation continuously increased from 0 to 60 minutes.
Conclusion: This scenario is false.
Final Answers:
- Melissa and Corey started on different trails: True
- Melissa hiked up the trail for a longer period of time than Corey: True
- Melissa and Corey crossed paths between 60 and 90 minutes: False
- Corey began his descent before Melissa: True
- As Melissa's time increased from 0 to 60 minutes, her elevation decreased: False
| Time (min) | Melissa's Elevation (feet) | Corey's Elevation (feet) |
|------------|-----------------------------|---------------------------|
| 0 | 8,342 | 10,004 |
| 30 | 9,550 | 11,432 |
| 60 | 11,239 | 12,921 |
| 90 | 12,921 | 11,075 |
| 120 | 12,921 | 10,004 |
1. Melissa and Corey started on different trails:
To check if they started on different trails, we compare their elevations at time 0 minutes:
- Melissa: 8342 feet
- Corey: 10004 feet
Since their elevations at the start are different, it is clear that they started on different trails.
Conclusion: This scenario is true.
2. Melissa hiked up the trail for a longer period of time than Corey:
To determine who hiked up the trail for a longer period, we need to find the duration for which their elevation was continuously increasing:
- Melissa's elevation increased from 0 to 90 minutes.
- Corey's elevation increased from 0 to 60 minutes, and then began to descend from 60 minutes to 120 minutes.
Therefore, Melissa hiked upward for the entire 90 minutes, while Corey hiked upward only for 60 minutes before descending.
Conclusion: This scenario is true.
3. Melissa and Corey crossed paths between 60 and 90 minutes:
To check if they crossed paths, we need to see if they had the same elevation at any time between 60 and 90 minutes:
- At 60 minutes: Melissa - 11,239 feet, Corey - 12,921 feet
- At 90 minutes: Melissa - 12,921 feet, Corey - 11,075 feet
Clearly, their elevations are never the same between 60 and 90 minutes.
Conclusion: This scenario is false.
4. Corey began his descent before Melissa:
To determine who began their descent first, we look at when each hiker's elevation started to decrease:
- Corey: His elevation starts to decrease after 60 minutes (it was highest at 60 minutes and then lower at 90 minutes).
- Melissa: Her elevation did not decrease; it stayed constant from 90 to 120 minutes.
Since Corey’s elevation started descending after 60 minutes and Melissa’s did not descend at any point, Corey began his descent before Melissa.
Conclusion: This scenario is true.
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased:
We need to check Melissa’s elevation from 0 to 60 minutes:
- At 0 minutes: 8342 feet
- At 30 minutes: 9550 feet
- At 60 minutes: 11239 feet
Melissa's elevation continuously increased from 0 to 60 minutes.
Conclusion: This scenario is false.
Final Answers:
- Melissa and Corey started on different trails: True
- Melissa hiked up the trail for a longer period of time than Corey: True
- Melissa and Corey crossed paths between 60 and 90 minutes: False
- Corey began his descent before Melissa: True
- As Melissa's time increased from 0 to 60 minutes, her elevation decreased: False
