Question 1209086
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Five workers have been hired to complete a job.  
If one additional worker is hired, they could complete the job 6 days earlier.  
If the job needs to be completed 32 days earlier, how many additional workers should be hired?
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                    Solve it step by step.


<pre>
      Step 1 - determine the number of days needed for 5 workers
               to complete the job.


Let d be the number of days for 5 workers to complete the job.

Then the entire job is 5d worker-days.


6 workers could complete the job in (d-6) days.

Hence, from this perspective, the entire work is  6*(d-6)  worker-days.


It gives us this equation

    5d = 6(d-6),

from which we get

     5d = 6d - 36  --->  36 = 6d - 5d  --->  36 = d.


Hence, 5 workers need 36 days to complete the job,  and the entire job is 5*36 = 180 worker-days.



      Step 2 - determine the number of workers needed 
               to complete the job in 32 days earlier.


The question wants the job be complete in 36-32 = 4 days.


It requires 180/4 = 45 workers.



      Step 3 - determine the number of additional workers 
               to be hired.


The number of additional workers is  45 - 5 = 40.


<U>ANSWER</U>.  40 additional workers should be hired to complete the job in 32 days earlier.
</pre>

Solved.