Determining the Number of Workers Needed to Complete a Project in a Specified Time
When dealing with work-related problems, it is often necessary to determine how many workers are needed to complete a specific task within a given time frame. This article explores the concept using a straightforward example, where 10 men working for 15 days complete a task. The challenge is to figure out how many men are required to finish the same task in 25 days. We will solve this problem using various methods to ensure a clear understanding of the underlying principles.
Understanding the Problem
The given scenario states that 10 men can complete a task in 15 days. The total man-days required to complete the task is calculated as 10 men x 15 days 150 man-days. Man-days represent the total amount of work done, considering the number of workers and the number of days they work.
Method 1: Direct Calculation
To find the number of men required to finish the same task in 25 days, we start with the total man-days required (150 man-days) and divide it by the new number of days (25 days).
Calculation: 150 man-days ÷ 25 days 6 men
This approach confirms that 6 men are needed to complete the task in 25 days.
Method 2: Inverse Relationship Between Workers and Days
The relationship between the number of workers and the time taken to complete a task is inverse. As the number of workers increases, the time required decreases, and vice versa.
We use the formula:
Original Work (10 men x 15 days) New Work (x men x 25 days)
Let's denote the number of men required to complete the task in 25 days as x.
Calculation: 10 men x 15 days 150 man-days 150 man-days x men x 25 days x 150 ÷ 25 6 men
This confirms that 6 men are needed to complete the task in 25 days.
Method 3: Using Proportional Reasoning
We can also use proportional reasoning to solve this problem. If 10 men working for 15 days complete the task, then we can determine the number of men needed for 25 days by proportionality.
Calculation: 10 men x 15 days 150 man-days For 25 days, we need x men such that 150 man-days x men x 25 days x 150 ÷ 25 6 men
This method also confirms that 6 men are required to complete the task in 25 days.
Conclusion
Understanding the inverse relationship between the number of workers and the time taken to complete a task is crucial for solving similar problems. The problem can be solved using direct calculation, inverse relationship, or proportional reasoning. In each method, the answer is consistently 6 men.
By applying these methods, we can effectively determine the number of workers needed to complete a project within a specified time frame. This knowledge is valuable in project management, workforce planning, and resource allocation.