Calculating Work Done by A, B, and C in a Collaborative Project: An SEO-Optimized Guide

Whether you are managing a team or simply curious about how collaborative work is calculated, understanding the work rates of individuals and how they contribute to a project is crucial. In this article, we will walk you through the process of determining how much work is completed when three individuals A, B, and C collaborate and then continue the project independently. This guide is designed to meet Google's advanced SEO standards and is filled with useful tips for effective web content creation.

Introduction to Work Rates

In this example, Team A, B, and C have different efficiencies in completing the same task. Specifically, Individual A can complete the work in 20 days, Individual B in 30 days, and Individual C in 60 days. Understanding how these individuals' efficiencies combine and change over time is essential for understanding the final outcome of their collaborative project.

Step-by-Step Solution

Step 1: Calculate the Daily Work Rates

To calculate the daily work rate for each individual, we first convert their completion times into daily contributions. Here are the daily work rates for A, B, and C:

A's daily work rate (frac{1}{20})

B's daily work rate (frac{1}{30})

C's daily work rate (frac{1}{60})

Step 2: Calculate the Total Work Done in the First 5 Days

When A, B, and C work together for the first 5 days, their combined work rate is as follows:

Combined work rate (frac{1}{20} frac{1}{30} frac{1}{60})

To add these fractions, we need a common denominator, which is 60. Converting each fraction:

(frac{1}{20} frac{3}{60}) (frac{1}{30} frac{2}{60}) (frac{1}{60} frac{1}{60})

Adding them together:

Combined work rate (frac{3}{60} frac{2}{60} frac{1}{60} frac{6}{60} frac{1}{10})

This means that together, they complete (frac{1}{10}) of the work in one day. Over 5 days:

Total work done 5 (times) (frac{1}{10} frac{5}{10} frac{1}{2})

Step 3: Remaining Work After A Leaves

After 5 days of working together, the remaining work is:

Remaining work 1 - (frac{1}{2} frac{1}{2})

Step 4: Work Done by B and C Together for the Next 5 Days

Now, B and C work together for the next 5 days. Their combined work rate is:

Combined work rate (frac{1}{30} frac{1}{60})

Converting to a common denominator of 60:

(frac{1}{30} frac{2}{60}) (frac{1}{60} frac{1}{60})

Adding them together:

Combined work rate (frac{2}{60} frac{1}{60} frac{3}{60} frac{1}{20})

Over 5 days:

Total work done 5 (times) (frac{1}{20} frac{5}{20} frac{1}{4})

After these 5 days, the remaining work is:

Remaining work (frac{1}{2} - frac{1}{4} frac{2}{4} - frac{1}{4} frac{1}{4})

Step 5: Work Done by C Alone for the Remaining Work

C then completes the remaining (frac{1}{4}) of the work independently. With C's daily work rate of (frac{1}{60}), the time C needs to complete (frac{1}{4}) of the work is calculated as follows:

C's time to complete (frac{1}{4}) of the work (frac{frac{1}{4}}{frac{1}{60}} frac{60}{4} 15) days

Step 6: Calculating the Portion of Work Done by C

To find the total work done by C, we add up her contributions from different parts of the project:

While A and B Worked: 5 days (times) (frac{1}{60} frac{5}{60} frac{1}{12}) While B Worked: 5 days (times) (frac{1}{60} frac{5}{60} frac{1}{12}) Independently: (frac{1}{4} frac{15}{60})

Total work done by C (frac{1}{12} frac{1}{12} frac{15}{60} frac{5}{60} frac{5}{60} frac{15}{60} frac{25}{60} frac{5}{12})

Final Answer: C's contribution to the total work is (frac{5}{12}).

Conclusion

Understanding the work rates and contributions of each team member is crucial for effective project management and task distribution. By following the steps outlined in this article, you can accurately determine the portions of work completed by each individual in a collaborative project, ensuring efficient and fair distribution of work.

Keywords

work rate, work distribution, collaborative problem solving