Question

A man can complete a job in 12 days. How many days will it take for 3 men to complete the same job, assuming they work at the same rate?

• A. 3
• B. 4
• C. 6
• D. 8

Hint:

For work problems, calculate the combined rate by adding individual rates, then use \( \text{Time} = \frac{1}{\text{Rate}} \), or divide total work by the number of workers.

Answer 1

The Correct Option is B

Determine the time required for 3 men to complete a job, given that 1 man can complete it in 12 days, assuming uniform work rates.

1. Core Principles:

- Work Efficiency: An individual's daily contribution is the inverse of their total completion time. For one man finishing in 12 days, his daily output is \( \frac{1}{12} \) of the job.
- Collective Effort: When individuals collaborate, their individual work rates are additive.
- Total Duration: The time to complete the task is the inverse of the combined daily work rate.

2. Provided Data:

- Time for one man = 12 days
- Number of workers = 3

3. Calculation of Combined Output and Duration:

- Daily work rate of one man = \( \frac{1}{12} \)
- Combined daily work rate of three men = \( 3 \times \frac{1}{12} = \frac{3}{12} = \frac{1}{4} \)
- Time for 3 men to complete the job = \( \frac{1}{\frac{1}{4}} = 4 \) days

Final Result:

The job will be completed by three men in 4 days.