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Efficiency Analysis of Workforce in Teamwork

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The efficiency and timely completion of a project are crucial in any team setting, particularly when multiple members with varying work rates are involved. This article explores the collaboration dynamics of three workers, A, B, and C, and calculates the optimal working time for each individual to independently complete a task.

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Problem Statement

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The problem at hand involves workers A, B, and C, where their combined work rates are given. Specifically, worker A can complete a work in 30 days, workers B and C together in 20 days, and workers A and B together can complete 2/3 of the work in 12 days. The aim is to determine the individual completion times for each worker and, more importantly, the remaining work completion time for C after A and B work together for a certain period.

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Calculation for Worker A

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Given that worker A can complete a work in 30 days, we can represent this as . By solving this, we get:

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Calculation for Worker B

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The total work rate for B and C working together is given by: . By using the equation , we can solve for b and c, yielding:

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After calculations, B takes to complete the work, and C takes to complete the work.

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Remaining Work for C

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When A and B work together for 12 days, they complete of the work. We need to determine the time for C to complete the remaining work. After A and B work for 12 days, they complete:

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24/60 of the work. Thus, the remaining work is , which means:

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C alone can complete it in 9 days. Therefore, the time required for C to complete the remaining work is .

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Conclusion

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This analysis demonstrates the importance of understanding the individual and collective work rates in team dynamics. By harnessing the strengths and compensating for the inefficiencies of each team member, projects can be completed more efficiently. The results suggest that while A, B, and C have different work rates, they can collectively complete a project in the optimal time, emphasizing the value of collaborative and efficient team management.