Question
Mountain climber Joe climbed to a mountain peak that was1200 feet above its base and 1500 feet east of its base. Mountain climber Bob climbed to a mountain peak that was 900 feet above its base and 1000 feet east of its base.
Who climbed a steeper mountain? Explain.
Who climbed a steeper mountain? Explain.
Answers
GPT-4o mini
To determine who climbed a steeper mountain, we can calculate the slope of each mountain using the formula for slope:
\[
\text{slope} = \frac{\text{rise}}{\text{run}}
\]
where "rise" is the vertical distance climbed, and "run" is the horizontal distance.
### For Joe:
- Rise: 1200 feet
- Run: 1500 feet
Calculating Joe's slope:
\[
\text{slope}_{\text{Joe}} = \frac{1200 \text{ ft}}{1500 \text{ ft}} = \frac{12}{15} = \frac{4}{5} = 0.8
\]
### For Bob:
- Rise: 900 feet
- Run: 1000 feet
Calculating Bob's slope:
\[
\text{slope}_{\text{Bob}} = \frac{900 \text{ ft}}{1000 \text{ ft}} = \frac{9}{10} = 0.9
\]
### Comparison:
- Joe's slope = 0.8
- Bob's slope = 0.9
Since a steeper slope indicates a greater vertical rise for a given horizontal distance, we can conclude that Bob climbed the steeper mountain because his slope (0.9) is greater than Joe's slope (0.8).
\[
\text{slope} = \frac{\text{rise}}{\text{run}}
\]
where "rise" is the vertical distance climbed, and "run" is the horizontal distance.
### For Joe:
- Rise: 1200 feet
- Run: 1500 feet
Calculating Joe's slope:
\[
\text{slope}_{\text{Joe}} = \frac{1200 \text{ ft}}{1500 \text{ ft}} = \frac{12}{15} = \frac{4}{5} = 0.8
\]
### For Bob:
- Rise: 900 feet
- Run: 1000 feet
Calculating Bob's slope:
\[
\text{slope}_{\text{Bob}} = \frac{900 \text{ ft}}{1000 \text{ ft}} = \frac{9}{10} = 0.9
\]
### Comparison:
- Joe's slope = 0.8
- Bob's slope = 0.9
Since a steeper slope indicates a greater vertical rise for a given horizontal distance, we can conclude that Bob climbed the steeper mountain because his slope (0.9) is greater than Joe's slope (0.8).