Describing a Possible Scenario for a Table:
| 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.
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 (2)
Melissa and Corey started at different elevations, indicating they began on different trails.
Melissa ascended for 90 minutes, while Corey ascended for only 60 minutes before descending, meaning Melissa hiked upwards longer.
Between 60 and 90 minutes, Melissa's and Corey's elevations crossed, indicating they crossed paths.
Corey started descending after 60 minutes, while Melissa stopped ascending after 90 minutes, so Corey descended first.
Therefore, the correct options 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, and Corey began his descent before Melissa. The answer is T r u e , T r u e , T r u e , T r u e , F a l se .
Explanation
Understanding the Problem We are given a table showing the elevation of two hikers, Melissa and Corey, at different times. We need to determine which of the given statements must be true based on the data in the table.
Analyzing Each Statement Let's analyze each statement:
Melissa and Corey started on different trails.
At time 0, Melissa's elevation is 8,342 feet, and Corey's elevation is 10,004 feet. Since their starting elevations are different, they must have started on different trails. This statement is TRUE.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa's elevation increases from 0 to 90 minutes (8,342 to 12,921 feet) and then remains constant from 90 to 120 minutes (12,921 feet). This means she stopped ascending after 90 minutes.
Corey's elevation increases from 0 to 60 minutes (10,004 to 12,921 feet) and then decreases from 60 to 120 minutes (12,921 to 10,004 feet). This means he started descending after 60 minutes.
Since Melissa hiked upwards for 90 minutes and Corey hiked upwards for only 60 minutes, Melissa hiked up the trail for a longer period of time than Corey. This statement is TRUE.
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. Corey is higher than Melissa.
At 90 minutes, Melissa's elevation is 12,921 feet, and Corey's elevation is 11,075 feet. Melissa is higher than Corey.
Since Corey was higher than Melissa at 60 minutes and Melissa was higher than Corey at 90 minutes, they must have crossed paths between 60 and 90 minutes. This statement is TRUE.
Corey began his descent before Melissa.
As determined in statement 2, Corey began his descent after 60 minutes, while Melissa stopped ascending after 90 minutes. Therefore, Corey began his descent before Melissa. This statement is TRUE.
As Melissa's time increased from 0 to 60 minutes, her elevation decreased.
At 0 minutes, Melissa's elevation is 8,342 feet.
At 60 minutes, Melissa's elevation is 11,239 feet.
Since her elevation increased from 8,342 to 11,239 feet, this statement is FALSE.
Conclusion Based on our analysis, the statements that must be true 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.
Corey began his descent before Melissa.
Examples
Understanding elevation changes during a hike can help you plan your trip effectively. For example, if you know the elevation profile of a trail, you can estimate how long it will take to reach certain points and how strenuous the hike will be. This information is crucial for ensuring your safety and enjoyment on the trail. Similarly, comparing the elevation profiles of two hikers can help determine who is ascending or descending faster, which can be useful in coordinating group hikes or understanding the dynamics of a race.
A device delivering a current of 15.0 A for 30 seconds moves approximately 2.81 × 1 0 21 electrons. This is calculated by first finding the total charge transferred and then dividing by the charge of a single electron. The total charge is 450 C , leading to the final count of electrons.
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