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?

LiIIiam0216 Mar 3, 2024

#2**+1 **

Let the time to complete the job with 5 workers = T days

So......the total man-days for the job is 5T

If one additional worker is hired, the man-days for the job is 6 (T - 8)

So....since the man-days will be the same for the job.....

5T = 6(T - 8)

5T = 6T - 48

48 = T

So the number of man-days to complete the job is 5(48) = 240

So.....to complete the job 28 days earlier

(number of workers needed) * ( 48 - 28) = 240

(number of workers needed) * (20) = 240

number of workers needed = 240 / 20 = 12

So.....(12 - 5) = 7 additional workers should be hired to complete the job 28 days earlier

CPhill Mar 4, 2024

#1**+1 **

How many additional workers should be hired?

**Hello Lilliam0216!**

I assume the 5 workers can complete the job in around 120 hours.

\(\psi =\frac{J}{5\cdot 120h}\\ J=5\cdot 120h\cdot \psi =(5+1)\cdot (120-8)\cdot \psi=(5+x)\cdot (120-28)\cdot \psi\\ 6\cdot 112=(5+x)\cdot 92\\ 672=460+92x\\ x=\frac{672-460}{92}=2.3\color{blue}\to 3\\ 6\cdot t=(5+\color{blue}3)\cdot 92\)

\(t=\frac{8\cdot 92}{6}=\color{blue}122\frac{2}{3}h\)

If the 5 workers completed the work in 122 2/3 hours, 3 additional workers should be hired to save 28 hours.

**An additional time specification is absolutely necessary for your question.**

** !**

asinus Mar 4, 2024

#2**+1 **

Best Answer

Let the time to complete the job with 5 workers = T days

So......the total man-days for the job is 5T

If one additional worker is hired, the man-days for the job is 6 (T - 8)

So....since the man-days will be the same for the job.....

5T = 6(T - 8)

5T = 6T - 48

48 = T

So the number of man-days to complete the job is 5(48) = 240

So.....to complete the job 28 days earlier

(number of workers needed) * ( 48 - 28) = 240

(number of workers needed) * (20) = 240

number of workers needed = 240 / 20 = 12

So.....(12 - 5) = 7 additional workers should be hired to complete the job 28 days earlier

CPhill Mar 4, 2024