Solving a Work and Men Problem with Algebraic Steps and SEO Optimization

Solving a Work and Men Problem with Algebraic Steps and SEO Optimization

SEO optimization is a crucial component for any web content, ensuring that it appeals to the Google algorithm and ranks well in search results. This article provides a detailed, SEO-friendly solution to a work and men problem, using algebraic steps to tackle the problem effectively. This content is designed to be informative, user-friendly, and keyword-rich, aiding in better SEO performance.

Introduction

The problem at hand revolves around the efficient completion of a specific piece of work under varying conditions. We will break down the process into clear, logical steps, using algebra to solve for the unknown variable x. Along the way, we will discuss how to optimize this content for SEO to ensure it ranks well in search results.

Step-by-Step Analysis

Step 1: Calculate the Total Work in Man-Days

First, we need to define the total amount of work in terms of man-days. Given that 40 men can complete the work in 48 days:

W Number of men times; Number of days 40 men times; 48 days 1920 man-days

Step 2: Calculate the Work Done by 64 Men in x Days

If 64 men work for x days, the amount of work they complete (W1) is:

W1 64 men times; x days 64x man-days

Step 3: Calculate the Remaining Work After x Days

The remaining work (R) after x days is:

R W - W1 1920 - 64x

Step 4: Work Done by 96 Men in 162/3 Days

After x days, 32 more men join the initial 64 men, making it 96 men. They complete the remaining work in 162/3 days. Converting 162/3 to an improper fraction, we get:

162/3 50/3 days

The amount of work done by 96 men in this time (W2) is:

W2 96 men times; 50/3 days 1600 man-days

Step 5: Set Up the Equation for the Remaining Work

Since the remaining work is equal to the work done in the last 162/3 days:

1920 - 64x 1600

Step 6: Solve for x

Rearranging the equation gives:

1920 - 1600 64x
320 64x
Now divide both sides by 64:
x 320 รท 64 5

Conclusion

The value of x is:

boxed{5}

Therefore, the 64 men worked for 5 days before the additional 32 men joined to complete the work. This step-by-step solution ensures clarity and makes the problem-solving process easily understandable.

SEO Optimization Tips

To optimize this content for SEO, ensure that each H2, H3, and paragraph is keyword-rich. Use primary keywords like 'work and men problem', 'algebraic solution', and 'man-days calculation' throughout the content. Incorporate meta tags, alt tags, and internal linking to boost SEO and improve user engagement. Include relevant images and videos to enhance the content, making it more engaging for users and search engines alike.

Final Thought

By following these steps and incorporating SEO best practices, the solution to the work and men problem becomes not only a mathematical exercise but also a well-optimized piece of content, ready to rank well in Google search results.