# It takes 12 men 5 days to complete a job. Determine how many days it would take 3 men to complete...

## Question:

It takes 12 men 5 days to complete a job. Determine how many days it would take 3 men to complete a job.

## Proportion:

When two ratios are equal to each other they are considered as proportions. It has many uses. It can be used to convert one unit to another. It can also be used to determine the amount of one component is needed for the other without changing the ratio.

It takes 12 men 5 days to complete a job, this means that {eq}\rm \dfrac {(5 \ days)(12 \ men)}{1 \ job} {/eq}. The ratio used is the product of the number of days and the number of men because the two factors affect how the job is done. Hence, to get how long it takes 3 men to complete a similar job, let {eq}x {/eq} be the number of days:

{eq}\begin{align} \rm \dfrac {(x \ days)(3 \ men)}{1 \ job} &= \rm \dfrac {(5 \ days)(12 \ men)}{1 \ job} \\ 3x &= 60 \\ x &= \dfrac {60} {3} \\ x &= 20 \end{align} {/eq}

This means that the same job would be finished by 3 men in {eq}\color{blue}{ \rm 20 \ days} . {/eq}