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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Problem Statement:**
William is staying in a cottage along a beautiful and straight shoreline. A point \( Q \) on the shoreline is located 3 kilometers east of the cottage, and an island is located 2 kilometers north of \( Q \). William plans to travel from the cottage to the island by some combination of walking and swimming. He can start to swim at any point \( P \) between the cottage and the point \( Q \). If he walks at a rate of 7 km/hr and swims at a rate of 5 km/hr, what is the minimum possible time it will take William to reach the island?
Enter an exact answer or round to the nearest hundredth of an hour.
**Diagram Description:**
- The diagram consists of a horizontal line representing the shoreline, measuring 3 km from the Cottage to \( Q \).
- A vertical line extends 2 km north from \( Q \) to represent the water distance to the Island.
- Points marked are the Cottage on the far left, \( Q \) on the far right, and the Island directly above \( Q \).
**Solution:**
Provide your answer below:
\[ \boxed{\,\,} \ \text{hours} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f7f5a9a-cde5-4f62-b382-ccc727ec6b9a%2F23e5acdd-5b8f-4a23-afc2-03813b69096b%2F1f35tbl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
William is staying in a cottage along a beautiful and straight shoreline. A point \( Q \) on the shoreline is located 3 kilometers east of the cottage, and an island is located 2 kilometers north of \( Q \). William plans to travel from the cottage to the island by some combination of walking and swimming. He can start to swim at any point \( P \) between the cottage and the point \( Q \). If he walks at a rate of 7 km/hr and swims at a rate of 5 km/hr, what is the minimum possible time it will take William to reach the island?
Enter an exact answer or round to the nearest hundredth of an hour.
**Diagram Description:**
- The diagram consists of a horizontal line representing the shoreline, measuring 3 km from the Cottage to \( Q \).
- A vertical line extends 2 km north from \( Q \) to represent the water distance to the Island.
- Points marked are the Cottage on the far left, \( Q \) on the far right, and the Island directly above \( Q \).
**Solution:**
Provide your answer below:
\[ \boxed{\,\,} \ \text{hours} \]
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