To determine which scenarios must be true based on the table, we need to analyze the given data at each time interval closely. Here are the answers to each of the given scenarios:
1. Melissa and Corey started on different trails.
- At 0 minutes, Melissa's elevation is 8,342 feet, while Corey's elevation is 10,004 feet.
- Since their starting elevations are different, they must have started on different trails.
- Therefore, 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 minutes to 90 minutes and remains constant from 90 to 120 minutes.
- Corey's elevation increases from 0 to 60 minutes and then decreases from 60 to 120 minutes.
- Melissa stayed at her highest elevation (12,921 feet) from 90 to 120 minutes, indicating she hiked up longer compared to Corey, who started descending at 60 minutes.
- Therefore, this statement is True.
3. Melissa and Corey crossed paths between 60 and 90 minutes.
- At 60 minutes, Melissa's elevation is 11,239 feet, and Corey's elevation is 12,921 feet.
- At 90 minutes, Melissa's elevation is 12,921 feet, and Corey's elevation is 11,075 feet.
- Between 60 and 90 minutes, Melissa's elevation increased past Corey's elevation, which decreased, indicating they crossed paths during this period.
- Therefore, this statement is True.
4. Corey began his descent before Melissa.
- Corey reaches his highest elevation (12,921 feet) at 60 minutes and then starts to descend.
- Melissa reaches her highest elevation (12,921 feet) at 90 minutes and stays there.
- Corey began his descent at 60 minutes, before Melissa reached her peak at 90 minutes.
- Therefore, this statement is False.
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased.
- Between 0 and 60 minutes, Melissa's elevation increases from 8,342 feet to 11,239 feet.
- Since her elevation is increasing rather than decreasing, this statement is False.
Based on the analysis, the results are:
1. True
2. True
3. True
4. False
5. False
So, the statements verified by the data 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.
These are the correct scenarios based on the given table.
