Answer :
We will use the nifty formula shown below to solve this rate-job problem.
[tex]\text{RWT}=J[/tex]Where
R is the rate
W is the number of workers
T is the time
J is the number of jobs
Here, it is given "12 assemblers can complete a certain job in 4 hours". Thus,
W = 12
J = 1
T = 4
Let's figure out the rate:
[tex]\begin{gathered} \text{RWT}=J \\ R(12)(4)=1 \\ R(48)=1 \\ R=\frac{1}{48} \end{gathered}[/tex]Now, we will again use the formula to see how long it will take "8 workers" to do the same job.
So,
W = 8
J = 1
T = ??
So,
[tex]\begin{gathered} \text{RWT}=J \\ (\frac{1}{48})(8)T=1 \\ \frac{8}{48}T=1 \\ T=\frac{1}{\frac{8}{48}} \\ T=\frac{48}{8} \\ T=6 \end{gathered}[/tex]Answer6 hours