Question

If 5 workers can complete a job in 12 days, how long will 8 workers take to complete the same job (assuming all work at the same rate)?

• A. 6 days
• B. 7.5 days
• C. 8 days
• D. 9 days

Hint:

For work problems, use the formula: \(\text{Workers} \times \text{Days} = \text{Constant}\). More workers reduce the time proportionally.

Answer 1

The Correct Option is B

Determine the duration for 8 workers to finish a task that 5 workers complete in 12 days. Assume uniform work rate among all workers.

1. Core Concepts:

- Work Unit: The total effort required for the task is constant.
- Worker Count (n): The number of individuals engaged in the task.
- Time (T): The duration to achieve task completion.
- Work Rate: The output of a single worker per day.
- An increase in the number of workers leads to a decrease in completion time, indicating an inverse relationship between workers and time when work rate is constant.

2. Provided Data:

\( n_1 = 5 \) workers
\( T_1 = 12 \) days (time for 5 workers)
\( n_2 = 8 \) workers
\( T_2 = ? \) (time for 8 workers)

3. Solution Methodology:

Step 1: Quantify total work in worker-days.
With 5 workers completing the task in 12 days, total work = \( 5 \text{ workers} \times 12 \text{ days} = 60 \) worker-days.
This signifies that 60 days of effort from a single worker are needed.

Step 2: Calculate the time for 8 workers to complete the same total work.
When 8 workers collaborate, they contribute 8 worker-days of effort daily.
Therefore, the required duration = \( \frac{\text{Total Work}}{\text{Worker Count}} = \frac{60 \text{ worker-days}}{8 \text{ workers}} = 7.5 \) days.

4. Conclusion:

The group of 8 workers will complete the task more rapidly than the group of 5 workers. The estimated completion time is 7.5 days, equivalent to 7 days and 12 hours.

Final Answer:

The job will be completed by 8 workers in 7.5 days.