A riverboat travels 69 km downstream in 3 hours. It travels 68 km upstream in 4 hours. Find the speed of the boat and the speed of the stream. The speed of the boat is and the speed of the stream is
A riverboat travels 69 km downstream in 3 hours. It travels 68 km upstream in 4 hours. Find the speed of the boat and the speed of the stream. The speed of the boat is and the speed of the stream is
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Problem Statement:
A riverboat travels 69 km downstream in 3 hours. It travels 68 km upstream in 4 hours. Find the speed of the boat and the speed of the stream.
### Tasks:
1. Determine the speed of the boat.
2. Determine the speed of the stream.
#### Answer Fields:
- The speed of the boat is: [Input Box]
- The speed of the stream is: [Input Box]
### Graphs/Diagrams:
There are no graphs or diagrams associated with this problem statement.
---
**Explanation:**
This problem can be solved using the concepts of relative speed in downstream and upstream motion. When the boat is traveling downstream, its speed is the sum of its still water speed and the stream speed. When traveling upstream, its speed is the difference between its still water speed and the stream speed.
Given:
- Downstream distance: 69 km
- Downstream time: 3 hours
- Upstream distance: 68 km
- Upstream time: 4 hours
Let:
- \( v_b \) be the speed of the boat in still water (in km/hr)
- \( v_s \) be the speed of the stream (in km/hr)
Equations:
\[ v_b + v_s = \frac{69}{3} \]
\[ v_b - v_s = \frac{68}{4} \]
These equations can be solved to find the respective speeds of the boat and the stream.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F006a35a3-e559-4cc9-aa53-746bb30a70e8%2F334ca2b6-94c5-43c9-98ff-3c74df8322c2%2Fn5t42fb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
A riverboat travels 69 km downstream in 3 hours. It travels 68 km upstream in 4 hours. Find the speed of the boat and the speed of the stream.
### Tasks:
1. Determine the speed of the boat.
2. Determine the speed of the stream.
#### Answer Fields:
- The speed of the boat is: [Input Box]
- The speed of the stream is: [Input Box]
### Graphs/Diagrams:
There are no graphs or diagrams associated with this problem statement.
---
**Explanation:**
This problem can be solved using the concepts of relative speed in downstream and upstream motion. When the boat is traveling downstream, its speed is the sum of its still water speed and the stream speed. When traveling upstream, its speed is the difference between its still water speed and the stream speed.
Given:
- Downstream distance: 69 km
- Downstream time: 3 hours
- Upstream distance: 68 km
- Upstream time: 4 hours
Let:
- \( v_b \) be the speed of the boat in still water (in km/hr)
- \( v_s \) be the speed of the stream (in km/hr)
Equations:
\[ v_b + v_s = \frac{69}{3} \]
\[ v_b - v_s = \frac{68}{4} \]
These equations can be solved to find the respective speeds of the boat and the stream.
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