Question

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?

Answer 1

It is given that the number of hours $h$ varies directly as the number of computers $c$ and inversely as the number of workers $w$ and$h=9$ when $c=12$ and $w=4$, therefore,

$h=\frac{kc}{w}\Rightarrow 9=\frac{k\times 12}{4}\Rightarrow 9=3k\Rightarrow k=\frac{9}{3}=3$

Thus, the general equation is $h=\frac{3c}{w}$.

Since $c=48$ and $h=8$, therefore,

$h=\frac{3c}{w}\Rightarrow 8=\frac{3\times 48}{w}\Rightarrow 8=\frac{144}{w}\Rightarrow 8w=144\Rightarrow w=\frac{144}{8}=18$

Hence, $18$ workers are needed to assemble $48$ computers in $8$ hours.