A Work Completed by 10 People in 14 Days - How Many Days Would It Take for 4 People?

The relationship between the number of workers and the time taken to complete a project is a fundamental concept in project management and labor productivity. Let's explore this through a specific example: if 10 people can complete a work in 14 days, how many days would it take for 4 people to complete the same work?

Calculation of Work Done in Person-Days

To solve this problem, we use the concept of person-days, which is a unit of work that measures the effort required by one person to complete a given task. Here, the total amount of work done can be calculated as follows:

Total Person-Days Required to Complete the Work

10 people x 14 days 140 person-days. This means that the total amount of work required is 140 person-days.

For 4 persons, the required days to complete the work would be:

Total person-days required to complete the work 140
For 4 persons, required days to complete the work 140 / 4 35 days.

Step-by-Step Breakdown

The total work can also be expressed in terms of a person doing the work. One person would take 140 days to complete the work by themselves.

Solution: If 4 people are working on the same work, the time required would be 140 / 4 35 days.

Relation to Work Efficiency

The calculation of work completion time with different team sizes demonstrates the inverse relationship between the number of workers and the time required to complete a project. As the number of workers increases, the days required to complete the work decrease proportionally, assuming each person works at the same rate.

Understanding Basic Work Rate

Alternatively, we can break it down using the work rate. One person completes 1/10 of the work in 14 days, meaning they complete 1/100 of the work per day. With 4 people working together, they complete 4/100 of the work per day, thus requiring 100 / 4 25 days to finish the work.

Therefore, even with a different number of workers, the total amount of work remains the same, and the time taken is inversely proportional to the number of workers.

Conclusion

Understanding the relationship between work completion time and team size is crucial for project management, resource allocation, and productivity optimization. Whether you have a large team or a small group, the principles of work rate and person-days can be used to predict and plan the completion times accurately.

By leveraging these concepts, organizations can efficiently manage their resources and ensure projects are completed within the desired timeframe.