Let's solve this problem step-by-step.
1. Understand the total amount of work:
- We know that 4 workers take 120 hours to complete the job.
- To find the total amount of work in "worker-hours," we multiply the number of workers by the number of hours:
[tex]\[
\text{Total work} = 4 \text{ workers} \times 120 \text{ hours} = 480 \text{ worker-hours}
\][/tex]
2. Determine the time required for 16 workers:
- We need to find out how long it will take for 16 workers to complete the same amount of work (480 worker-hours).
- Since the total amount of work remains the same, we divide the total work by the number of workers:
[tex]\[
\text{Time} = \frac{480 \text{ worker-hours}}{16 \text{ workers}} = 30 \text{ hours}
\][/tex]
So, it would take 16 workers 30 hours to complete the job.
Therefore, the correct answer is:
C) 30 hours
