Question

Mr. Specter designed the layout for a factory. The roof of the factory has an elevation of 56.2 feet, and the floor of the lowest level has an elevation of -15.3 feet. A pulley is installed on an outer wall at an approximate elevation equal to 1/4 of the total height of the factory. The factory office floor is located 5.5 feet above the pulley.

What is the approximate elevation of the factory office floor?

Answer 1

To find the approximate elevation of the factory office floor, we first need to calculate the total height of the factory from the floor of the lowest level to the roof.

1. **Calculate the total height of the factory**:
- The elevation of the roof is 56.2 feet.
- The elevation of the lowest floor is -15.3 feet.
- Total height = Roof elevation - Lowest floor elevation
\[
\text{Total height} = 56.2 - (-15.3) = 56.2 + 15.3 = 71.5 \text{ feet}
\]

2. **Calculate the elevation of the pulley**:
- The pulley is installed at an elevation equal to 1/4 of the total height.
\[
\text{Pulley elevation} = \frac{1}{4} \times 71.5 = 17.875 \text{ feet}
\]

3. **Calculate the elevation of the factory office floor**:
- The factory office floor is located 5.5 feet above the pulley.
\[
\text{Office floor elevation} = \text{Pulley elevation} + 5.5
\]
\[
\text{Office floor elevation} = 17.875 + 5.5 = 23.375 \text{ feet}
\]

Thus, the approximate elevation of the factory office floor is **23.4 feet** (rounded to one decimal place).