12 worker take 4 hours to complete a job.How long would it take 15 workers to complete the job?

Options

A. 2 hrs
B. 3.2 hrs
C. 3 .5 hrs
D. 3 hrs

Answer

To solve the problem step by step, we will use the unitary method.

### Step 1: Understand the given information
We know that:
- 12 workers take 4 hours to complete a job.

### Step 2: Find the total work done in worker-hours
First, we need to calculate the total amount of work done in terms of worker-hours.
Total work = Number of workers × Time taken
Total work = 12 workers × 4 hours = 48 worker-hours.

### Step 3: Determine the time taken by 15 workers
Now, we need to find out how long it will take for 15 workers to complete the same amount of work (48 worker-hours).
Let the time taken by 15 workers be \( t \) hours.
Using the formula for total work:
Total work = Number of workers × Time taken
48 worker-hours = 15 workers × \( t \) hours.

### Step 4: Solve for \( t \)
To find \( t \), we rearrange the equation:
\[ t = \frac{48 \text{ worker-hours}}{15 \text{ workers}} \]
Calculating this gives:
\[ t = \frac{48}{15} \]
\[ t = 3.2 \text{ hours} \]

### Step 5: Convert the decimal into hours and minutes
Now, we convert 0.2 hours into minutes:
0.2 hours × 60 minutes/hour = 12 minutes.

### Final Answer
Thus, it will take 15 workers 3 hours and 12 minutes to complete the job.

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