# 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?

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:

$4 \cdot 12 = 48$ computers could be assembled by $4$ workers in $4 \cdot 9 = 36$ hours.

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

$48$ computers could be assembled by $\frac{9}{2} \cdot 4 = 18$ workers in $\frac{2}{9} \cdot 36 = 8$ hours.