Your college quadrangle is 86 meters long and 65 meters wide. When you are late for class, you can walk (well, run) at 8 miles per hour. You are at one corner of the quad and your class is at the directly opposite corner. How much time can you save by cutting across the quad rather than walking around the edge? s (Round your answer to two decimal places.)
Your college quadrangle is 86 meters long and 65 meters wide. When you are late for class, you can walk (well, run) at 8 miles per hour. You are at one corner of the quad and your class is at the directly opposite corner. How much time can you save by cutting across the quad rather than walking around the edge? s (Round your answer to two decimal places.)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![**Problem Description:**
Your college quadrangle is 86 meters long and 65 meters wide. When you are late for class, you can walk (or run) at 8 miles per hour. You are at one corner of the quad, and your class is at the directly opposite corner. How much time can you save by cutting across the quad rather than walking around the edge?
**Answer Format:**
\[ \text{s (Round your answer to two decimal places.)} \]
**Understanding the Problem:**
To solve this problem, you need to calculate the time taken to walk around the two sides of the rectangle and the time saved by walking directly across the diagonal.
**Steps to Solution:**
1. **Calculate the Distance Around the Edge:**
- The distance around the edge is the sum of the length and the width of the rectangle, multiplied by 2.
- \( \text{Distance around the edge} = 86 + 65 = 151 \) meters.
2. **Find the Diagonal Distance:**
- Use the Pythagorean theorem to calculate the diagonal distance.
- \( \text{Diagonal} = \sqrt{86^2 + 65^2} \).
3. **Convert Speed from Miles per Hour to Meters per Second:**
- 1 mile = 1609.34 meters.
- Speed in meters per second = \( 8 \times \frac{1609.34}{3600} \).
4. **Calculate Time for Each Path:**
- Time to walk around the edge:
- \( \text{Time around} = \frac{151}{\text{speed in meters per second}} \).
- Time to walk across the diagonal:
- \( \text{Time diagonal} = \frac{\text{Diagonal}}{\text{speed in meters per second}} \).
5. **Calculate Time Saved:**
- \( \text{Time saved} = \text{Time around} - \text{Time diagonal} \).
Round the final answer to two decimal places for the time saved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c9a3da8-b443-4c7b-9ddb-d4ba4f71dd14%2F7c1a1a96-3dae-49a9-8856-4d430aaa933d%2Ft4e67pp_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
Your college quadrangle is 86 meters long and 65 meters wide. When you are late for class, you can walk (or run) at 8 miles per hour. You are at one corner of the quad, and your class is at the directly opposite corner. How much time can you save by cutting across the quad rather than walking around the edge?
**Answer Format:**
\[ \text{s (Round your answer to two decimal places.)} \]
**Understanding the Problem:**
To solve this problem, you need to calculate the time taken to walk around the two sides of the rectangle and the time saved by walking directly across the diagonal.
**Steps to Solution:**
1. **Calculate the Distance Around the Edge:**
- The distance around the edge is the sum of the length and the width of the rectangle, multiplied by 2.
- \( \text{Distance around the edge} = 86 + 65 = 151 \) meters.
2. **Find the Diagonal Distance:**
- Use the Pythagorean theorem to calculate the diagonal distance.
- \( \text{Diagonal} = \sqrt{86^2 + 65^2} \).
3. **Convert Speed from Miles per Hour to Meters per Second:**
- 1 mile = 1609.34 meters.
- Speed in meters per second = \( 8 \times \frac{1609.34}{3600} \).
4. **Calculate Time for Each Path:**
- Time to walk around the edge:
- \( \text{Time around} = \frac{151}{\text{speed in meters per second}} \).
- Time to walk across the diagonal:
- \( \text{Time diagonal} = \frac{\text{Diagonal}}{\text{speed in meters per second}} \).
5. **Calculate Time Saved:**
- \( \text{Time saved} = \text{Time around} - \text{Time diagonal} \).
Round the final answer to two decimal places for the time saved.
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