Direct and Inverse Variation: How many workers are needed to assemble 48 computers in 8 hours?

The number of hours needed to assemble computers varies directly as the number of computers and inversely as the number of workers. If 4 workers can assemble 12 computers in 9 hours, how many workers are needed to assemble 48 computers in 8 hours?

The answer on the worksheet says 41 workers, but I get 18. Who's right?

1 Answer
Jan 27, 2018

The worksheet is in error - the number of workers required is 18

Explanation:

Given:

4 workers can assemble 12 computers in 9 hours.

Since the number of hours is directly proportional to the number of computers:

4 * 12 = 48 computers could be assembled by 4 workers in 4 * 9 = 36 hours.

Since the number of hours is inversely proportional to the number of workers:

48 computers could be assembled by 9/2 * 4 = 18 workers in 2/9 * 36 = 8 hours.