Efficiency in Work: A Detailed Efficacy Analysis with SEO Optimization

This article will explore the mathematical problem of calculating work efficiency based on a given scenario. We will delve into how to determine individual and combined work rates, calculate the work done, and find the time required to complete the remaining task. By the end of this article, you will have a clear understanding of work efficiency in a practical context.

Understanding the Task: A, B, and C's Work Rates

In a given scenario, A can complete a specific piece of work in 40 days. B, being 25% more efficient than A, and C, being 28% more efficient than B, work together for 5 days. The objective is to calculate the remaining work and determine how much time B will need to complete the rest of the work alone.

Step 1: Determining the Work Rate of A

A can complete the work in 40 days. Therefore, A's work rate is:

Work rate of A  1 / 40 (work per day)

Step 2: Calculating the Work Rate of B

B is 25% more efficient than A. Hence, B's work rate is:

Work rate of B  (1 / 40) * 1.25  1 / 32 (work per day)

Step 3: Determining the Work Rate of C

C is 28% more efficient than B. Therefore, C's work rate is:

Work rate of C  (1 / 32) * 1.28  1 / 25 (work per day)

Step 4: Combining the Work Rates of A, B, and C

The combined work rate of A, B, and C when working together is:

Combined work rate  (1 / 40)   (1 / 32)   (1 / 25)

Converting to a common denominator (800), we get:

Combined work rate  (20 / 800)   (25 / 800)   (32 / 800)  77 / 800 (work per day)

Step 5: Calculating the Work Done in 5 Days

In 5 days, the amount of work completed by A, B, and C together is:

Work done in 5 days  5 * (77 / 800)  385 / 800  77 / 160 (work done)

Step 6: Calculating the Remaining Work

The remaining work is the difference between the total work (1) and the work done in 5 days:

Remaining work  1 - 77 / 160  83 / 160 (work remaining)

Step 7: Determining the Time Required for B to Complete the Remaining Work

Since B's work rate is 1 / 32 work per day, the time required for B to complete the remaining work is:

Time taken by B  (83 / 160) / (1 / 32)  (83 * 32) / 160  2656 / 160  16.6 (days)

Therefore, B will take approximately 16.6 days to complete the remaining work alone.

SEO Optimization and Keyword Integration

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Conclusion

This detailed analysis showcases the practical application of work rates and efficiency in problem-solving scenarios. By applying these concepts, you can enhance your understanding of work efficiency and how to optimize such scenarios for better performance. In the context of SEO, integrating relevant keywords will help improve the visibility and ranking of your content on search engines.