Question 1079215
<pre>
I believe that 7 more workers are needed:
</pre>
5 men are hired to complete a job. If one more man is hired, the 
job can be completed 8 days earlier. Assuming that all the men 
work at the same rate, how many more men should be hired so that 
the job can be completed 28 days earlier? 
<pre><b>
Use the worker-time-job formula, which is:

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

where

W<sub>1</sub> = the number of workers in the first situation.
T<sub>1</sub> = the number of time units (days in this case) in the first situation.
J<sub>1</sub> = the number of jobs in the first situation.

W<sub>2</sub> = the number of workers in the second situation.
T<sub>2</sub> = the number of time units (days in this case) in the second situation.
J<sub>2</sub> = the number of jobs in the second situation.

W<sub>1</sub> =  5             W<sub>2</sub> = 6     
T<sub>1</sub> =  x days        T<sub>2</sub> = x-8 days 
J<sub>1</sub> =  1             J<sub>2</sub> = 1

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

{{{(5*x)/1}}}{{{""=""}}}{{{(6*(x-8))/1}}}

{{{5*x}}}{{{""=""}}}{{{6*x-48}}}

{{{-x}}}{{{""=""}}}{{{-48}}}

{{{x}}}{{{""=""}}}{{{48}}}

So it takes 48 days for 5 workers to do the job.

Now we use the worker-time-job formula again with N more workers than 5,
or 5+N workers, and 28 days less than 48 or 10 days.

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

this time with

W<sub>1</sub> = 5             W<sub>2</sub> = 5+N     
T<sub>1</sub> = 48 days       T<sub>2</sub> = 48-28=20 days 
J<sub>1</sub> = 1             J<sub>2</sub> = 1

{{{(5*48)/1}}}{{{""=""}}}{{{((5+N)*20)/1}}}

{{{240}}}{{{""=""}}}{{{20(5+N)}}}

{{{240}}}{{{""=""}}}{{{100+20N}}}

{{{140}}}{{{""=""}}}{{{20N}}}

{{{7}}}{{{""=""}}}{{{N}}}

So 7 more workers will be needed.

Edwin</pre>