How Many Days Will 8 Men Working 12 Hours Complete a Job That 10 Men Consumed 60 Man-Hours Per Day in 8 Days?
The question at hand is a classic problem in labor productivity and work rate calculations. The goal is to determine how long it will take a different number of workers, with a different working schedule, to complete the same job that a previous group of workers finished. This problem is often used in project management, workforce planning, and even in understanding the dynamics of labor market efficiency. Let's break down the problem and solve it step by step.
Understanding Man-Hours and Work Rate
In labor productivity terms, man-hours refer to the total number of hours spent by a labor force on a particular task. This concept helps in understanding the output of a worker or a group of workers in terms of time spent. The work rate is the speed at which a job is done, measured by the number of man-hours required to complete the job. This is crucial in determining the efficiency of a work team and in planning future labors based on historical data.
Step 1: Determine the Total Work in Man-Hours
Let's start by calculating the total amount of work in man-hours for the first group of workers.
Group 1:
Number of men: 10 Hours per day: 6 Days: 8The total work can be calculated as follows:
[ text{Total work} 10 text{men} times 6 text{hours/day} times 8 text{days} 480 text{man-hours} ]
Step 2: Calculate the Time Taken by the Second Group of Workers
Now, let's move on to the second group of workers.
Number of men: 8 Hours per day: 12 Let#39;s denote the number of days required to complete the job as ( D )The total work done by the second group can be expressed as:
[ 8 text{men} times 12 text{hours/day} times D text{days} 96D text{man-hours} ]
Step 3: Set the Total Work Equal to the Previous Calculation
Since both groups are working on the same job, we can set the total work done by the second group equal to the total work done by the first group:
[ 96D 480 ]
Step 4: Solve for ( D )
To find the value of ( D ), we solve the equation:
[ D frac{480}{96} 5 text{days} ]
Conclusion: It will take 5 days for 8 men working 12 hours a day to complete the same job.
Further Insights and Considerations
Understanding the concept of man-hours and work rates is crucial for project management. The calculation we just performed allows us to predict and optimize the workload for future projects. However, the problem statement provided some ambiguity. In practical scenarios, the units of time (hours or days) should be clearly defined, as using both in a single scenario can lead to confusion.
If the initial job was spread out over 8 days with 10 men working 6 hours each day, the total man-hours would be 480. In the second scenario, for 8 men to complete the same job, the reduced workload duration (5 days) with the same total man-hours still hold true.
Summary
By analyzing the total work in man-hours, we determined that 8 men working 12 hours a day would complete the job in 5 days. This illustrates the importance of understanding work rates and labor productivity in project estimation and planning.