Solving Work Rate Problems: A Comprehensive Guide

When tackling problems involving work rates, such as '4 men or 7 women can do a work in 90 days. How many days will 8 men and 7 women together take to complete the same work?,' we can apply a systematic approach to break down the problem and solve it effectively. Understanding the concept of man-days and woman-days can be crucial in not only solving the problem but also in optimizing your SEO for relevant keywords. In this guide, we will explore the solution step-by-step and provide tips for SEO optimization.

Step 1: Understanding Man-Days and Woman-Days

Man-days and woman-days are units of work done by a single worker in a single day. For instance, if 4 men can complete a task in 90 days, the total work can be expressed as 360 man-days. Similarly, if 7 women can complete the same task in 90 days, the total work can be expressed as 630 woman-days.

Step 2: Convert Work into Units of Time

By converting the given information into consistent units, we can establish the work rate. Let's solve the problem step-by-step:

Step 3: Determine the Work Rate

Given:

4 men can complete the work in 90 days, which means 4 men * 90 days 360 man-days. 7 women can complete the work in 90 days, which means 7 women * 90 days 630 woman-days.

Let's set the work done in man-days and woman-days equal:

4m * 90 360 → 4m 4 → m 1 (1 man can complete the work in 90 days). 7w * 90 630 → 7w 7 → w 1 (1 woman can complete the work in 90 days).

From the above steps, we see that 1 man's work in one day is equivalent to 1 woman's work in one day.

Step 4: Calculate the Combined Work Rate

Now, let's determine the combined work rate for 8 men and 7 women:

8 men and 7 women together can do:

8 * 1 (work of men per day) 7 * 1 (work of women per day) 8 7 15 units of work per day.

Step 5: Determine the Time to Complete the Work

To find out how many days it will take for 8 men and 7 women to complete the work, we use the combined work rate:

Total work 360 man-days 630 woman-days.

Days to complete the work Total Work / Combined Work Rate

Days to complete the work 360 / 15 24 days.

Conclusion

Thus, 8 men and 7 women together will take 24 days to complete the work.

SEO Optimization Tips and Keywords

To optimize your content for search engines, make sure to include relevant keywords strategically in your text. For instance, the keywords 'work rate,' 'man-days,' and 'woman-days' are highly relevant to the topic at hand. Additionally, including detailed problem-solving steps and examples can enhance the value of your content and improve its chances of being ranked higher.

Keyword Optimization

work rate man-days woman-days

By following these guidelines and using the appropriate keywords, you can increase the visibility and relevance of your content in search engine results.