Question

hiking elevation (feet)time (min)\tmelissa\tcorey0\t8,342\t10,00430\t9,550\t11,43260\t11,239\t12,92190\t12,921\t11,075120\t12,921\t10,004assuming two hikers begin at a trail start, which scenarios must be true based on the table? check all that apply.☐ melissa and corey started on different trails.☐ melissa hiked up the trail for a longer period of time than corey.☐ melissas and coreys elevations were same at some time between 60 and 90 minutes.☐ corey began his descent before melissa.☐ as melissas time increased from 0 to 60 minutes, her elevation decreased.

Explanation:

1. At time 0 (start), Melissa's elevation is 8,342 ft and Corey's is 10,004 ft, so they started on different trails.
2. At 60 minutes, Melissa is at 11,239 ft (lower than Corey's 12,921 ft); at 90 minutes, Melissa is at 12,921 ft (higher than Corey's 11,075 ft). By the Intermediate Value Theorem, their elevations must have crossed (been equal) between 60-90 minutes.
3. Corey's elevation peaks at 60 minutes (12,921 ft) and drops after that, while Melissa's elevation increases until 90 minutes, so Corey began descending first.
4. Melissa's elevation increases from 8,342 to 11,239 ft between 0-60 minutes, so the final statement is false.
5. We only have elevation at 30-minute intervals; we cannot confirm Melissa hiked uphill longer than Corey, so this is not a must-be-true statement.

Answer:

• Melissa and Corey started on different trails.
• Melissa's and Corey's elevations were same at some time between 60 and 90 minutes.
• Corey began his descent before Melissa.