Understanding the Impact of Labor and Work Hours on Construction Projects

Construction projects often involve careful planning and allocation of resources to ensure successful completion within a set timeframe. One critical factor in this planning is determining how the number of workers and their working hours affect the overall duration of the project. Letrsquo;s explore a practical scenario regarding the building of a small house.

Case Study: Building a Small House

Suppose a group of construction workers can build a small house in 30 days, working 8 hours a day.

The question we are addressing is, if we have 20 workers who work 6 hours a day, how many days will it take to build the same house?

Mathematical Approach to Solve the Problem

To solve this problem, we can use the principle of proportionality. The general formula is:

[ text{Man-Days-Hours} text{Work} ]

Where:

[ text{M} ] Number of Men [ text{D} ] Number of Days [ text{H} ] Number of Hours per day

Letrsquo;s break down the given data and apply it to our problem.

Step 1: Calculate Total Man-Hours for Original Case

The original group consists of [ M ] workers who work for 30 days, 8 hours per day. Therefore, the total man-hours for the original group is:

[ text{Total Man-Hours} M times 30 times 8 ]

Step 2: Calculate Required Man-Hours for New Group

The new group consists of 20 workers who work 6 hours a day. Letrsquo;s assume it takes [ N ] days for the new group to complete the same work. Therefore, the total man-hours for the new group is:

[ text{Total Man-Hours} 20 times 6 times N ]

Step 3: Set Up and Solve the Proportionality Equation

Since the total work (man-hours) remains the same, we can set up the following equation:

[ M times 30 times 8 20 times 6 times N ]

Solving for [ N ] gives:

[ N frac{30 times 8 times M}{20 times 6} frac{240M}{120} ]

[ N 2M ]

Since we are given that [ M 1 ] (1 original worker), we substitute [ M ] and find:

[ N 2 times 30 div 5 div 6 2 times 5 div 6 frac{10}{6} frac{160}{9} ]

Final Answer

Therefore, it will take the 20 workers working 6 hours per day approximately 17 and 7/9 days to build the same small house.

Conclusion

This example demonstrates the importance of understanding how the number of workers and their working hours impact the completion time of construction projects. By using mathematical principles, we can optimize labor efforts and allocate resources more effectively, ensuring both efficiency and timely project completion.