Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $8$ days earlier. If the job needs to completed $28$ days earlier, how many additional workers should be hired?

Answer 1

Let $m$ be the number of additional workers that should be hired. Since one additional worker could complete the job $8$ days earlier, it would take $n-8$ days if $n+1$ workers completed the job. Since the job needs to be completed $28$ days earlier, we have $n^2 - 8n = n^2 - 28.$ Simplifying the equation gives $28 - 8n = 0,$ or $n = \frac{28}{8} = \boxed{3.5}.$