A jet's speed in still air is 240 mph. One day it flew 700 miles with a tailwind and then returned the same distance against the wind. The total flying time was 6 hours. Use the following equation to find the speed of the wind (w). =6 700 240+w ·+ 700 240-w
A jet's speed in still air is 240 mph. One day it flew 700 miles with a tailwind and then returned the same distance against the wind. The total flying time was 6 hours. Use the following equation to find the speed of the wind (w). =6 700 240+w ·+ 700 240-w
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.2: Applied Problems
Problem 37E
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Question
![### Problem Statement
A jet's speed in still air is 240 mph. One day it flew 700 miles with a tailwind and then returned the same distance against the wind. The total flying time was 6 hours. Use the following equation to find the speed of the wind (w).
\[
\frac{700}{240 + w} + \frac{700}{240 - w} = 6
\]
### Explanation
In this problem, we need to determine the speed of the wind, denoted as \( w \), which affects the speed of the jet during its flight with and against the wind.
1. **Variables and Equations:**
- **Jet's speed in still air (\( v \))**: 240 mph.
- **Distance traveled with tailwind**: 700 miles.
- **Distance traveled against the wind**: 700 miles.
- **Total flying time**: 6 hours.
2. **Understanding the equation:**
- The term \( \frac{700}{240 + w} \) represents the time taken to travel 700 miles with the tailwind, where \( (240 + w) \) is the effective speed of the jet with the wind.
- The term \( \frac{700}{240 - w} \) represents the time taken to travel 700 miles against the wind, where \( (240 - w) \) is the effective speed of the jet against the wind.
- The sum of these two times is given as 6 hours.
### Solution Strategy
1. **Equation Setup:**
- You have two rational expressions added to make up 6 hours.
- The two expressions depend on the speed of the wind, \( w \).
2. **Solving the Equation:**
- Identify a common denominator for the rational expressions, which can help simplify the equation.
- Use algebraic methods to isolate the variable \( w \) and solve for its value.
This approach will help you find the exact speed of the wind that affects the jet's flight time as described.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee316dc0-9fcf-44c0-a9c4-799945d7ab8e%2F132cc112-4db3-4a4f-859a-d0d10896120e%2F5bh3ull_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A jet's speed in still air is 240 mph. One day it flew 700 miles with a tailwind and then returned the same distance against the wind. The total flying time was 6 hours. Use the following equation to find the speed of the wind (w).
\[
\frac{700}{240 + w} + \frac{700}{240 - w} = 6
\]
### Explanation
In this problem, we need to determine the speed of the wind, denoted as \( w \), which affects the speed of the jet during its flight with and against the wind.
1. **Variables and Equations:**
- **Jet's speed in still air (\( v \))**: 240 mph.
- **Distance traveled with tailwind**: 700 miles.
- **Distance traveled against the wind**: 700 miles.
- **Total flying time**: 6 hours.
2. **Understanding the equation:**
- The term \( \frac{700}{240 + w} \) represents the time taken to travel 700 miles with the tailwind, where \( (240 + w) \) is the effective speed of the jet with the wind.
- The term \( \frac{700}{240 - w} \) represents the time taken to travel 700 miles against the wind, where \( (240 - w) \) is the effective speed of the jet against the wind.
- The sum of these two times is given as 6 hours.
### Solution Strategy
1. **Equation Setup:**
- You have two rational expressions added to make up 6 hours.
- The two expressions depend on the speed of the wind, \( w \).
2. **Solving the Equation:**
- Identify a common denominator for the rational expressions, which can help simplify the equation.
- Use algebraic methods to isolate the variable \( w \) and solve for its value.
This approach will help you find the exact speed of the wind that affects the jet's flight time as described.
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