Question

hiking elevation (feet)
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
assuming 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:

Step1: Analyze starting - point

At time = 0, Melissa's elevation is 8342 feet and Corey's is 10004 feet. But this doesn't mean they are on different trails as they could start at different elevations on the same trail.

Step2: Analyze hiking time

The table shows time intervals up to 120 minutes for Melissa and 120 minutes for Corey. There is no indication that Melissa hiked longer.

Step3: Analyze equal - elevation

Melissa's elevation is increasing and Corey's first increases and then decreases. By the intermediate - value theorem, since Melissa's elevation goes from 8342 to 12921 and Corey's goes from 10004 to 11075 (and back to 10004), their elevations must be the same at some time between 60 and 90 minutes.

Step4: Analyze descent start

Corey's elevation starts to decrease from 12921 at 60 minutes to 11075 at 90 minutes, while Melissa's elevation is still increasing from 11239 at 60 minutes to 12921 at 90 minutes. So Corey began his descent before Melissa.

Step5: Analyze Melissa's elevation change

As Melissa's time increased from 0 to 60 minutes, her elevation increased from 8342 to 11239, not decreased.

Answer:

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