# If 9 assemblers can complete a certain job in 4 hours, how long will the same job take if the...

## Question:

If 9 assemblers can complete a certain job in 4 hours, how long will the same job take if the number of assemblers is cut back to 6?

## Finding Time to Complete a Job

A given number of workers can complete a job in a given period of time. Then we cut back the number of workers. Using ratios and proportions we find the amount of time it will take in this case when the number of workers is cut back back by about a third. Ratios and proportions play an important role in areas of Mathematics such as Algebra, Geometry and Trigonometry.

Since 9 assemblers can complete the job in 4 hours, therefore it takes 9 x 4 = 36 assembler-hours to complete this job.

If the number of assemblers were reduced down to 6 then if they needed x hours to complete the job, the job would take 6x assembler-hours to finish.

Equating the quantities above for the completion of the job gives us the equation

{eq}\displaystyle 6x=36 \implies x = \frac {36}{6} =6. {/eq}

It takes 6 assemblers 6 hours to get the same job done. 