The Empire State Building is not only one of the most farnous buildings
in New York, It’s one of the most fomous buildings in the U.S. and even
in the world. At the time of Its opening, It stood as the tallest building
in the world. Its art deco style, height, and observation decks make it a
popular tourist attraction.
The empire state building has 102 floors and the top floor reaches
1,250 feet. Assume all floors are the same height. You get in the
elevator on the first floor and someone pushes the button for the 37 th
floor. You get there and now you start traveling down to the 22nd floor!
Findly you make your way up to the 102nd floor. Make a segment that
shows each stop and find the total distance traveled to the nearest
tenth.

Question

UpStudy AI · Accepted Answer

Certainly! Let's break down the elevator journey in the Empire State Building step by step and calculate the total distance traveled.

### **Given:**
- **Total Floors:** 102
- **Total Height:** 1,250 feet
- **Floors Visited:** 1st → 37th → 22nd → 102nd

### **Assumptions:**
- All floors are of equal height.

### **Step 1: Calculate Height per Floor**

To find the height of each floor:

1. **Determine the number of intervals between floors:**
   - Since the building has 102 floors, there are **101 intervals** between the 1st and 102nd floors.

2. **Calculate height per floor:**
   $$
   \text{Height per floor} = \frac{\text{Total Height}}{\text{Number of Intervals}} = \frac{1,250 \text{ ft}}{101} \approx 12.376 \text{ ft/floor}
   $$

### **Step 2: Map the Elevator Journey**

Let's outline each segment of the journey:

| **Stop** | **Floor Number** | **Direction** | **Number of Floors Traveled** | **Distance (ft)** |
|----------|------------------|---------------|-------------------------------|-------------------|
| 1        | 1st              | —             | —                             | 0                 |
| 2        | 37th             | Up            | 36                            | $$36 \times 12.376 \approx 446.14$$ ft |
| 3        | 22nd             | Down          | 15                            | $$15 \times 12.376 \approx 185.64$$ ft |
| 4        | 102nd            | Up            | 80                            | $$80 \times 12.376 \approx 990.08$$ ft |
| **Total**| —                | —             | **131 floors**                | **$$446.14 + 185.64 + 990.08 \approx 1,621.86$$ ft** |

### **Step 3: Calculate Total Distance Traveled**

Summing up the distances:

$$
\text{Total Distance} = 446.14 \text{ ft} + 185.64 \text{ ft} + 990.08 \text{ ft} \approx 1,621.86 \text{ ft}
$$

**Rounded to the nearest tenth:**

$$
\text{Total Distance} \approx 1,621.9 \text{ feet}
$$

### **Summary**

- **Total Floors Traveled:** 131
- **Total Distance Traveled:** **1,621.9 feet**

This calculation accounts for ascending to the 37th floor, descending to the 22nd floor, and finally ascending to the 102nd floor, ensuring each movement between floors is accurately represented based on the uniform floor height.
The total distance traveled is approximately 1,621.9 feet.

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