In a two-story home, the basement floor is 10 feet below the ground, and the attic floor is 24 feet above the ground. Find the distance in height between the two floors.
The Correct Answer and Explanation is:
To find the height difference between the basement floor and the attic floor in a two-story home, we need to calculate the total vertical distance between these two points.
Solution
- The basement floor is 10 feet below ground, which means it is at -10 feet (since it’s below the zero level, or ground level).
- The attic floor is 24 feet above the ground level, so it’s at +24 feet.
The total distance between the two floors can be found by calculating the difference between these two levels:
[
\text{Distance} = \text{Attic level} – \text{Basement level}
]
Substitute the values:
[
\text{Distance} = 24 – (-10) = 24 + 10 = 34 \text{ feet}
]
So, the distance in height between the two floors is 34 feet.
Explanation
In this problem, we are given two different heights with respect to ground level: one below the ground and one above it. The ground level is our zero point, so anything below it is negative, and anything above it is positive. This setup makes it easy to apply basic principles of distance by considering how far each point is from the ground in opposite directions.
The concept here involves subtracting the basement level from the attic level. Since the basement level is negative (-10 feet), subtracting a negative number (24 – (-10)) turns into addition: 24 + 10. This operation works because when we move from a negative height to a positive one, we’re effectively covering the distance below the ground, plus the distance above.
The height between any two points on a vertical plane can be found similarly: take the absolute difference of their heights, which gives the distance. This method can be applied in various real-world situations, like calculating the distance between floors in a building or comparing elevations. This question demonstrates a basic yet essential use of positive and negative numbers to calculate vertical distances accurately.