Contractor Steve agreed to complete a job in 30 days. After 6 days he found that the 8 people assigned to the work had already done 1/3 of the job. If everyone works at the same rate, what is the least number of people he must keep on the job to ensure that the job will be completed on time?

 May 22, 2020

First you need to figure out how much work each person does. 8 people did 1/3 of the job in 6 days.  If the same 8 people continued to work on the job, they would finish the job in 18 days (3x6).  That means each person contributed 2 1/4% of the job each day (18/8).  Now, the job is 1/3 complete and we're assuming that the contractor isn't trying to finish sooner than 30 days.  Now you can solve for the number of people needed to do the work in 24 days.  The equation is X people x .0225 x 24 days = .66 [that's x number of people needed times each person doing .0225 or 2.25% of the work per day times 24 days equals 2/3 or 66% of the work that remains].  In a 24 day period, each person will complete 54% of the work (2.25%x24).  So you need at least two people to finish the work in 24 days.

Hope this helps, whymenotsmart^m^.

 May 22, 2020

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