ACT Math · Ratios, rates, and percents

4 workers can complete a job in 10 hours. Working at the same rate per worker, how long would 5 workers take to complete the same job?

4 workers can complete a job in 10 hours. Working at the same rate per worker, how long would 5 workers take to complete the same job?

Answer and explanation

Answer: F: 8 hours

The total work is fixed: 44 workers for 1010 hours is 4⋅10=404\cdot10=40 worker-hours. With 55 workers, each doing the same amount of work per hour, the time is 405=8\frac{40}{5}=8 hours, choice F. More workers means less time, which is inverse variation. Choice H (1212) and choice J (12.512.5) increase the time when workers are added, which cannot be right. Choice G (8.58.5) is close but does not follow from the constant-work relationship. The product of workers and time stays 4040.

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