A group of hikers begins an uphill hike from a location that is 500 feet above sea level. Their elevation increases by 20 feet for every minute they hike. At the same time, a second group of hikers begins a downhill hike from a location 1,500 feet above sea level. Their elevation decreases by 30 feet for every minute they hike.

How long will it take for the two groups of hikers to reach the same elevation?

A. 20 minutes
B. 40 minutes
C. 100 minutes
D. 900 minutes

It will take 20 minutes for the two groups of hikers to reach the same elevation, with one group ascending from 500 feet and the other descending from 1,500 feet above sea level.

Explanation:

The question asks how long it will take for two groups of hikers to reach the same elevation, with one group starting at 500 feet above sea level and ascending at a rate of 20 feet per minute, and the other group starting at 1,500 feet above sea level and descending at a rate of 30 feet per minute.

Let's set up an equation to solve for the time 't' when both groups will have the same elevation. For the ascending group: Elevation1 = 500 + 20t. For the descending group: Elevation2 = 1500 - 30t.

We can find the time 't' when Elevation1 equals Elevation2:
500 + 20t = 1500 - 30t
50t = 1000
t = 20 minutes.

Therefore, it will take 20 minutes for the two groups of hikers to be at the same elevation.