If took 12 men 5 hours to build an airstrip. Working at the same rate, how many additional men could have been hired in order for the job to have taken 1 hour less?

Options

A. Two
B. Three
C. Four
D. Six

Answer

To solve the problem step by step, we need to determine how many additional men are required to complete the airstrip in 4 hours instead of 5 hours.

### Step 1: Understand the initial conditions
We know that 12 men take 5 hours to build the airstrip.

### Step 2: Calculate the total work done
The total work done can be calculated in terms of "man-hours."
- Total work = Number of men × Number of hours
- Total work = 12 men × 5 hours = 60 man-hours

### Step 3: Determine the new time frame
We want to complete the same work in 1 hour less, which means we need to finish the work in 4 hours.

### Step 4: Set up the equation for the new scenario
Let \( x \) be the additional men hired. Therefore, the total number of men working now will be \( 12 + x \).

The work done in the new scenario can also be expressed as:
- Total work = (Number of men) × (Number of hours)
- Total work = (12 + x) men × 4 hours

### Step 5: Set the equation equal to the total work
Since the total work remains the same (60 man-hours), we can set up the equation:
\[ (12 + x) \times 4 = 60 \]

### Step 6: Solve for \( x \)
1. Expand the equation:
\[ 48 + 4x = 60 \]
2. Isolate \( 4x \):
\[ 4x = 60 - 48 \]
\[ 4x = 12 \]
3. Divide by 4:
\[ x = \frac{12}{4} = 3 \]

### Conclusion
Thus, the number of additional men required is \( x = 3 \).