Calculating Remaining Work and Effort Distribution Among Workers
Calculating Remaining Work and Effort Distribution Among Workers
In this scenario, we are dealing with a problem where multiple workers collaborate on a task, but their performance changes over time. Understanding how to calculate the remaining amount of work and distribute the remaining effort can be crucial for project planning and resource allocation. Let's break down the problem step by step.
Initial Setup and Work Distribution
Start with the premise that a task can be completed by 3 people in 10 days. This equates to a total of 30 person-days, where each person contributes 1 person-day per day for 10 days.
Mathematically, we can express this as:
3 people 10 days 30 person-days
First Phase of Work
The first 3 days see all 3 people working. The amount of work completed during this period is:
3 3 1 person-day 9 person-days
Since each person contributes 1 person-day per day, the fraction of the task completed in the first 3 days is:
9 person-days 1/30 per person-day 9/30 of the task
Second Phase of Work
After the first 3 days, one person leaves, and the remaining two people continue working for another 3 days. The amount of work completed in this phase is:
2 3 1 person-day 6 person-days
Adding this to the previous 9 person-days, the total amount of work completed is:
9 person-days 6 person-days 15 person-days
The fraction of the task completed so far is:
15 person-days 1/30 per person-day 15/30 or 1/2 of the task
Remaining Work and Final Effort
Since 1/2 of the task is completed, the remaining work is also 1/2. The third person will complete this remaining half of the task alone. The required number of days for the third person to finish the remaining work is:
(1/2 of the task) 30 person-days (1 person 15 days
Therefore, it takes 15 days for the third person to complete the remaining work.
Alternative Methods and Reasoning
Alternatively, we can consider the work as consisting of 30 subtasks, each taking one day for one person to complete. After the first 3 days, 9 subtasks are completed, leaving 21 subtasks. After the next 3 days, 6 more subtasks are completed, leaving 15 subtasks. These 15 subtasks, which total the remaining half of the work, will take the third person 15 days to complete.
Another approach involves considering the total work as 30 person-days. In the first 3 days, 9 person-days are completed. In the next 3 days, another 6 person-days are completed, bringing the total to 15 person-days. The remaining 15 person-days of work are completed by the third person, taking 15 days.
Summary and Keywords
The problem illustrates the importance of understanding how distributed work and changing workforce impacts the completion of a project. Key takeaways include the use of person-days as a unit of work, the impact of changing workforce, and the need to redistribute work based on remaining effort.