Step 1: Define the total work in terms of "man-days."

If four men working full-time can complete the work in 42 days, then the total work required is:

$$ \text{Total Work} = 4 \times 42 = 168 \text{ man-days} $$

This means that the job requires a total of 168 man-days.

Step 2: Calculate the daily work rate when one man is working half-time.

Now, if three men work full-time and one man works half-time, their combined daily work rate is:

$$ \text{Daily Work Rate} = 3 + 0.5 = 3.5 \text{ men per day} $$

Step 3: Find the time required to complete the job with the new work rate.

We divide the total work by the daily work rate:

$$ \text{Time} = \frac{\text{Total Work}}{\text{Daily Work Rate}} = \frac{168}{3.5} $$

Step 4: Simplify the division:

$$ \text{Time} = 48 \text{ days} $$