Let's carefully analyze the data provided and address each statement one by one based on the hiking elevations of Melissa and Corey over time.
### Data Provided
| Time (min) | Melissa | Corey |
|------------|---------|--------|
| 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 |
### Analyzing Each Statement
#### 1. Melissa and Corey started on different trails.
- At time 0 min, Melissa's elevation is 8,342 feet, and Corey's elevation is 10,004 feet.
- Since they started at different elevations, they must have started on different trails.
- Conclusion: This statement is true.
#### 2. Melissa hiked up the trail for a longer period of time than Corey.
- Melissa's elevation increases consistently from 0 min to 90 min, indicating she is hiking up the trail.
- Corey’s elevation increases from 0 min to 60 min, peaks at 60 min, and then decreases from 60 min to 120 min.
- Melissa hiked up continuously for the first 90 minutes, while Corey started descending after 60 minutes.
- Conclusion: This statement is true.
#### 3. Melissa and Corey crossed paths between 60 and 90 minutes.
- At 60 min, Melissa's elevation is 11,239 feet, and Corey's elevation is 12,921 feet.
- At 90 min, Melissa's elevation is 12,921 feet, and Corey's elevation is 11,075 feet.
- Since Melissa's elevation at 90 min is the same as Corey's at 60 min, and Corey's descent passes within the range of Melissa's ascent, they must have crossed paths between 60 and 90 minutes.
- Conclusion: This statement is true.
#### 4. Corey began his descent before Melissa.
- Corey's elevation decreases between 60 and 120 minutes, indicating he started descending before 120 minutes.
- Melissa's elevation stays steady at 12,921 feet from 90 to 120 minutes, indicating she did not descend during the time period provided.
- Conclusion: This statement is true.
#### 5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased.
- From 0 to 60 minutes, Melissa's elevation increased from 8,342 feet to 11,239 feet.
- Her elevation did not decrease during this period; it increased.
- Conclusion: This statement is false.
### Summary
Based on the analysis, we can conclude the following about the given scenarios:
1. Melissa and Corey started on different trails. (True)
2. Melissa hiked up the trail for a longer period of time than Corey. (True)
3. Melissa and Corey crossed paths between 60 and 90 minutes. (True)
4. Corey began his descent before Melissa. (True)
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased. (False)
Therefore, the true scenarios are:
- Melissa and Corey started on different trails.
- Melissa hiked up the trail for a longer period of time than Corey.
- Melissa and Corey crossed paths between 60 and 90 minutes.
- Corey began his descent before Melissa.
