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# help algebra

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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?

Mar 3, 2024

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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

Mar 4, 2024
edited by CPhill  Mar 5, 2024

#1
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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.

!

Mar 4, 2024
#2
+129829
+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
edited by CPhill  Mar 5, 2024