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?
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
The worksheet is in error - the number of workers required is
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.
