Calculation and Analysis of Work Efficiency - A Comprehensive Guide
Understanding work efficiency is crucial for effective resource utilization in various industries. This article explores a specific problem involving two workers, A and B, to determine their individual work rates. By breaking down the problem step-by-step, we will calculate how many days worker B alone would need to complete the entire task.
Problem Statement
The given problem states that A and B together can complete a piece of work in 30 days. Worker A worked for 16 days, and then B alone finished the remaining work in 44 days. We need to determine how many days B would take to complete the entire work alone.
Step-by-Step Solution
Let's denote the work done by A per day as A and the work done by B per day as B.
Step 1 - Expressing Combined Work Rate
The combined work rate of A and B is given by:
A B Work per day to complete the entire work in 30 days 1/30
Step 2 - Individual Contributions
A worked for 16 days, so the work done by A during this period is:
16A
B worked alone for the remaining period, which is 44 days, so the work done by B during this period is:
44B
The combined work done by A and B is equal to 1 (the entire work), which leads to:
16A 44B 1
Step 3 - Combining the Equations
We also know that:
A B 1/30
Let's denote the work rates of A and B as RA and RB respectively. We have:
RA RB 1/30
From the combined work rate equation:
16RA 44RB 1
Substituting RA from the first equation:
16(1/30 - RB) 44RB 1
This simplifies to:
16/30 - 16RB 44RB 1
16/30 28RB 1
28RB 1 - 16/30
28RB 14/30
RB 14/30 * 1/28
RB 1/60
Since RB 1/60, it follows that:
RA 1/60
Therefore, both A and B have the same work rate of 1/60.
Step 4 - Calculating Individual Work Time
To find how many days B would take to complete the entire work alone:
Time taken by B 1/RB 1/1/60 60 days
Hence, worker B alone can finish the entire work in 60 days.
Conclusion
Understanding work rates and their implications is essential for effective project management and workforce planning. The problem presented here showcases a methodical approach to solving work-related problems, highlighting the significance of individual work rates in collaborative tasks.
Further Reading
For more in-depth analysis on work efficiency, visit [Further Reading Link] to explore similar problems and get comprehensive guides on work rate calculations.