Solving a Work and Time Problem Using Algebraic Equations for SEO Optimization

Optimizing content for search engines like Google requires not only adherence to their algorithms but also a structured and well-organized presentation of information. This article aims to provide a clear and SEO-friendly solution to a work and time problem, using algebraic equations and optimization strategies. The problem involves determining how long it will take for 5 men and 15 women to complete a certain piece of work given the efficiency of a group of men and women working together.

Introduction to the Problem

Let’s denote the work done by one man in one day as M and the work done by one woman in one day as W.

Step 1: Setting Up Equations Based on the Given Information

The first group consists of 8 men and 12 women working for 9 days to complete the work. The second group comprises 10 men and 20 women working for 6 days to achieve the same result.

8 men and 12 women working for 9 days: 8M 12W times 9 1 quad text{where 1 represents the whole work} 10 men and 20 women working for 6 days: 10M 20W times 6 1

Step 2: Simplifying the Equations

From the first equation, simplifying by dividing all terms by 4: 2M 3W frac{1}{36} From the second equation, simplifying by dividing all terms by 10: M 2W frac{1}{60}

Step 3: Solving the System of Equations

Now we can solve equations 3 and 4 simultaneously.

From equation 4: M frac{1}{60} - 2W Substituting M in equation 3: 2 left(frac{1}{60} - 2W right) 3W frac{1}{36} frac{2}{60} - 4W 3W frac{1}{36} frac{1}{30} - W frac{1}{36} -W frac{1}{36} - frac{1}{30} -frac{1}{180} W frac{1}{180} Substituting W back into equation 4 to find M: M 2 left(frac{1}{180} right) frac{1}{60} M frac{2}{180} frac{1}{60} M frac{2}{180} frac{3}{180} M frac{3}{180} - frac{2}{180} frac{1}{180}

Step 4: Calculating the Work Done by 5 Men and 15 Women

Using the values of M and W, we can calculate the work done by 5 men and 15 women in one day: 5M 15W 5 left(frac{1}{180} right) 15 left(frac{1}{180} right) frac{5}{180} frac{15}{180} frac{20}{180} frac{1}{9}

This means that 5 men and 15 women can complete (frac{1}{9}) of the work in one day.

Step 5: Calculating the Total Time Taken

If 5 men and 15 women can complete (frac{1}{9}) of the work in one day, the total time taken to complete the work is:

text{Time} frac{1}{frac{1}{9}} 9 text{ days}

Therefore, 5 men and 15 women will take 9 days to complete the work.

Optimization and SEO for Search Engines

To ensure this article ranks well on search engines like Google, it's essential to include keywords in headings, titles, and throughout the content. Specific keywords such as 'algebraic equations', 'work and time problems', and 'optimization' should be strategically placed to enhance the article's SEO.

Conclusion

By following a structured approach to solving work and time problems and optimizing the content for search engines, we can ensure that the information is accessible, well-organized, and optimized for maximum visibility. This article provides a clear and SEO-friendly solution to the given problem, making it a valuable resource for anyone seeking to learn or teach optimization strategies.