Question

for every 300 feet, a person travels up a mountain the temperature drops by 1 F. If the temperature is 78 F. at the base of a 6270-foot mountain what is the temperature at the peak?

Answer 1

To find the temperature at the peak of the mountain, we calculate the number of 300-foot segments in the mountain's height, then determine the total temperature drop by multiplying the number of segments by 1 F per segment, and subtract that from the initial temperature to find that the peak temperature is approximately 57 F.

Step-by-step explanation:

The student has asked: 'For every 300 feet, a person travels up a mountain the temperature drops by 1 F. If the temperature is 78 F at the base of a 6270-foot mountain, what is the temperature at the peak?'

To solve this, we'll first determine how many 300-foot segments there are in 6270 feet. We'll use the formula:

1. Number of segments = Total feet / Feet per segment
2. Number of segments = 6270 / 300
3. Number of segments = 20.9 (approximately)

Since the temperature drops 1 F for each 300-foot segment, we'll multiply the number of segments by the temperature drop per segment.

1. Total temperature drop = Number of segments × Temperature drop per segment
2. Total temperature drop = 20.9 × 1 F
3. Total temperature drop ≈ 21 F

Finally, we'll subtract this temperature drop from the initial temperature at the base of the mountain to find the temperature at the peak.

1. Temperature at peak = Initial temperature - Total temperature drop
2. Temperature at peak = 78 F - 21 F
3. Temperature at peak ≈ 57 F