Answer :
Let's break down each statement based on the provided table to solve this problem step-by-step.
### Table Data Recap
[tex]\[ \begin{array}{|c|c|c|} \hline \multicolumn{3}{|c|}{\text{Hiking Elevation (feet)}} \\ \hline \text{Time (min)} & \text{Melissa} & \text{Corey} \\ \hline 0 & 8,342 & 10,004 \\ \hline 30 & 9,550 & 11,432 \\ \hline 60 & 11,239 & 12,921 \\ \hline 90 & 12,921 & 11,075 \\ \hline 120 & 12,921 & 10,004 \\ \hline \end{array} \][/tex]
### Verifying Each Statement
1. Melissa and Corey started on different trails.
- Time 0: Melissa's elevation = 8,342 feet, Corey's elevation = 10,004 feet.
- Since their starting elevations are different, they indeed started on different trails.
- This statement is true.
2. Melissa hiked up the trail for a longer period of time than Corey.
- Both Melissa and Corey reach their maximum elevation at around 60 minutes.
- Melissa continues at her peak elevation (12,921 feet) from 60 to 120 minutes.
- Corey starts descending after 60 minutes, as seen from his elevation dropping from 12,921 feet at 60 minutes to 11,075 feet at 90 minutes.
- Thus, Corey's ascent period ends at 60 minutes, while Melissa continues ascending (or at least not descending) for a longer period.
- This statement is true.
3. Melissa and Corey crossed paths between 60 and 90 minutes.
- We need to check if there is any time between 60 and 90 minutes where their elevations are the same.
- Melissa: 60 minutes = 11,239 feet, 90 minutes = 12,921 feet
- Corey: 60 minutes = 12,921 feet, 90 minutes = 11,075 feet
- There is no time between 60 and 90 minutes where their elevations are equal.
- This statement is false.
4. Corey began his descent before Melissa.
- Corey starts descending after 60 minutes (from 60 to 90 minutes).
- Melissa maintains her maximum elevation of 12,921 feet from 60 to 120 minutes, showing no signs of descent during this period.
- Hence, Corey began descending before Melissa.
- This statement is true.
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased.
- Time from 0 to 60 minutes for Melissa:
- 0 min: 8,342 feet
- 30 min: 9,550 feet
- 60 min: 11,239 feet
- Her elevation increased each time.
- This statement is false.
### Conclusion
The true statements based on the provided table are:
1. Melissa and Corey started on different trails.
2. Melissa hiked up the trail for a longer period of time than Corey.
4. Corey began his descent before Melissa.
The false statements are:
3. Melissa and Corey crossed paths between 60 and 90 minutes.
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased.
### Table Data Recap
[tex]\[ \begin{array}{|c|c|c|} \hline \multicolumn{3}{|c|}{\text{Hiking Elevation (feet)}} \\ \hline \text{Time (min)} & \text{Melissa} & \text{Corey} \\ \hline 0 & 8,342 & 10,004 \\ \hline 30 & 9,550 & 11,432 \\ \hline 60 & 11,239 & 12,921 \\ \hline 90 & 12,921 & 11,075 \\ \hline 120 & 12,921 & 10,004 \\ \hline \end{array} \][/tex]
### Verifying Each Statement
1. Melissa and Corey started on different trails.
- Time 0: Melissa's elevation = 8,342 feet, Corey's elevation = 10,004 feet.
- Since their starting elevations are different, they indeed started on different trails.
- This statement is true.
2. Melissa hiked up the trail for a longer period of time than Corey.
- Both Melissa and Corey reach their maximum elevation at around 60 minutes.
- Melissa continues at her peak elevation (12,921 feet) from 60 to 120 minutes.
- Corey starts descending after 60 minutes, as seen from his elevation dropping from 12,921 feet at 60 minutes to 11,075 feet at 90 minutes.
- Thus, Corey's ascent period ends at 60 minutes, while Melissa continues ascending (or at least not descending) for a longer period.
- This statement is true.
3. Melissa and Corey crossed paths between 60 and 90 minutes.
- We need to check if there is any time between 60 and 90 minutes where their elevations are the same.
- Melissa: 60 minutes = 11,239 feet, 90 minutes = 12,921 feet
- Corey: 60 minutes = 12,921 feet, 90 minutes = 11,075 feet
- There is no time between 60 and 90 minutes where their elevations are equal.
- This statement is false.
4. Corey began his descent before Melissa.
- Corey starts descending after 60 minutes (from 60 to 90 minutes).
- Melissa maintains her maximum elevation of 12,921 feet from 60 to 120 minutes, showing no signs of descent during this period.
- Hence, Corey began descending before Melissa.
- This statement is true.
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased.
- Time from 0 to 60 minutes for Melissa:
- 0 min: 8,342 feet
- 30 min: 9,550 feet
- 60 min: 11,239 feet
- Her elevation increased each time.
- This statement is false.
### Conclusion
The true statements based on the provided table are:
1. Melissa and Corey started on different trails.
2. Melissa hiked up the trail for a longer period of time than Corey.
4. Corey began his descent before Melissa.
The false statements are:
3. Melissa and Corey crossed paths between 60 and 90 minutes.
5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased.
