ASVAB · Ratios, Proportions, and Rates

If 3 workers can complete a job in 8 hours, how long would it take 4 workers, assuming they all work at the same rate?

Correct answer

6 hours

  1. A 6 hours
  2. B 8 hours
  3. C 10.7 hours
  4. D 12 hours

Why this is the answer

This is an inverse proportion: more workers means less time. The total work is 3 workers × 8 hours = 24 worker-hours. With 4 workers, time = 24 worker-hours ÷ 4 workers = 6 hours. In inverse-proportion (work-rate) problems, the product of workers and time stays constant for the same job. Compute the total worker-hours, then divide by the new number of workers. Four workers finish the job in 6 hours, which makes sense because adding a worker should reduce the time, not increase it.
Source: ASVAB AR, Inverse Proportion Work