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\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{ Hiking Elevation (feet) } \\
\hline Time [tex]$( min )$[/tex] & Melissa & 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{tabular}

Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.

A. Melissa and Corey started on different trails.

B. Melissa hiked up the trail for a longer period of time than Corey.

C. Melissa and Corey crossed paths between 60 and 90 minutes.

D. Corey began his descent before Melissa.

E. As Melissa's time increased from 0 to 60 minutes, her elevation decreased.



Answer :

GinnyAnswer
Let's analyze each statement one by one based on the provided table of hiking elevations:

1. Melissa and Corey started on different trails:
- Looking at the initial elevations at time 0, Melissa's elevation is 8342 feet, and Corey’s elevation is 10004 feet.
- Since their starting elevations are different, they must have started on different trails.
- This statement is true.

2. Melissa hiked up the trail for a longer period of time than Corey:
- Melissa’s elevation increased from 8342 feet at time 0 to 12921 feet at time 120. From the data, it shows she hiked up continuously without descending.
- Corey's elevation increased from 10004 feet at time 0 to 12921 feet at time 60; however, between time 60 and time 120, his elevation decreased from 12921 feet to 10004 feet.
- Since Melissa hiked up to her maximum elevation for a longer duration (120 minutes) compared to Corey (60 minutes), Melissa hiked up for a longer time.
- This statement is true.

3. Melissa and Corey crossed paths between 60 and 90 minutes:
- Checking elevations at 60 minutes, Melissa’s elevation is 11239 feet, and Corey’s elevation is 12921 feet.
- Checking elevations at 90 minutes, Melissa’s elevation is 12921 feet, and Corey’s elevation is 11075 feet.
- The elevations at the specific times (60 and 90 minutes) show that they did not have the same elevation at any point between 60 and 90 minutes.
- This statement is false.

4. Corey began his descent before Melissa:
- Corey reached his maximum elevation of 12921 feet at 60 minutes and then started descending.
- Melissa reached her maximum elevation of 12921 feet at 90 minutes and did not descend.
- Thus, Corey began his descent before Melissa.
- This statement is true.

5. As Melissa's time increased from 0 to 60 minutes, her elevation decreased:
- Melissa’s elevation increased from 8342 feet at time 0 to 11239 feet at time 60.
- Her elevation did not decrease during this time; it continuously increased.
- This statement is false.

In summary, the scenarios that must be true based on the table are:

- Melissa and Corey started on different trails.
- Melissa hiked up the trail for a longer period of time than Corey.
- Corey began his descent before Melissa.

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