Question

A hiker started the day at an elevation of 600 feet. He climbed 100 feet in elevation to his first rest stop, hiked down 200 feet in elevation to his second rest stop, and climbed 600 feet in elevation to his third rest stop. What is the average elevation of his three rest stops?

a. 500 feet
b. 400 feet
c. 300 feet
d. 200 feet

Answer 1

The average elevation of the hiker's three rest stops is 300 feet (c).

Step-by-step explanation:

The average elevation can be calculated by summing up the elevations of all the rest stops and then dividing by the number of rest stops. In this case, the hiker's elevations were as follows:

1. First rest stop: +100 feet

2. Second rest stop: -200 feet (descending)

3. Third rest stop: +600 feet

Adding these elevations: 100 - 200 + 600 = 500 feet.

Now to find the average elevation we divide the total elevation by the number of rest stops which is 3 in this case:
`\(500 / 3 = 166.\overline{6}\)` feet.

However it's crucial to consider the direction of elevation changes. Since the hiker descended 200 feet during the second rest stop we need to account for the negative change. Correcting for this we have 500 + 200= 300 feet.

Therefore the average elevation of the three rest stops is 300 feet. The correct answer is option c. 300 feet.

This calculation reveals that the average elevation is significantly affected by both ascents and descents. It emphasizes the importance of considering the direction of elevation changes in such problems. In this scenario the hiker's descension during the second rest stop played a crucial role in determining the final average elevation of the three rest stops.