### Problem StatementA 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).\[\frac{700}{240 + w} + \frac{700}{240 - w} = 6\]### ExplanationIn 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 Strategy1. **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.

In this question , we will find the value of '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

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 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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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.

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