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Math  /  Geometry

QuestionQuestion 10 Pause Zoom
A mountain climber is climbing from the top of a 12,000 -foot peak to the top of a 14,000 -foot peak. The horizontal distance between the two peaks is 3,000 feet. What is the average slope to get from the first peak to the second peak?

Studdy Solution

STEP 1

1. The problem involves calculating the slope between two peaks.
2. The vertical change in height is from 12,000 feet to 14,000 feet.
3. The horizontal distance between the two peaks is 3,000 feet.
4. The slope is defined as the ratio of the vertical change to the horizontal change.

STEP 2

1. Determine the vertical change in height.
2. Use the slope formula to calculate the average slope.

STEP 3

Calculate the vertical change in height between the two peaks. The first peak is at 12,000 feet and the second peak is at 14,000 feet. The vertical change is:
Vertical change=14,000−12,000 \text{Vertical change} = 14,000 - 12,000

STEP 4

Use the slope formula, which is the ratio of the vertical change to the horizontal change. The formula for slope m m is:
m=Vertical changeHorizontal change m = \frac{\text{Vertical change}}{\text{Horizontal change}}
Substitute the values:
m=14,000−12,0003,000 m = \frac{14,000 - 12,000}{3,000}

STEP 5

Simplify the expression to find the slope:
m=2,0003,000 m = \frac{2,000}{3,000} m=23 m = \frac{2}{3}
The average slope to get from the first peak to the second peak is:
23 \boxed{\frac{2}{3}}

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