SOLUTION: 5 men are hired to complete a job. If one more man is hired, the job can be completed 8days earlier. Assuming that all men work at the same rate, how many more men should be hired

Let the rate of 1 man be r.

So the rate of the 5 men is 5r 

Since time = production/rate = (1 job)/(5r),

The 5 men could do the job in 1/(5r) days

That makes 6 men, whose rate is 6r.
Since time = production/rate = (1 job)/(6r),
The 6 men could do the job in 1/(6r) days

So 1/(6r) is 8 days less than 1/(5t), or

1/(6r) = 1/(5r) - 8

Multiply thru by LCD = 30r

    5 = 6 - 240r
   -1 = -240r
1/240 = r  <-- the rate of one man

That makes the rate of 5 men be 5/240,
or 1/48, that's 1 job per 48 days, so the 
5 men could finish 1 job in 48 days.  

Let the number of men that must be hired be n

Then there will be 5+n men working

So the rate of 5+n men is (5+n)r = (5+n)(1/240) = (5+n)/240 

Since time = production÷rate = (1 job)÷((5+n)/240) = 1×(240/(5+n) =
          240/(5+n)

So 240/(5+n) is 28 days less than the 48 days it would
take the 5 men, or 20 days.

240/(5+n) = 20
      240 = 20(5+n)
      240 = 100+20n
      140 = 20n
        7 = n

So 7 more men must be hired.

Edwin