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# i don't get this

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Engineer Marvin calculated that a certain construction project can be finished in 200 days by 30 workers. The project started with 30 workers. At the end of 90 days, 10 workers were fired. The remaining workers continued the work for 30 days. Then 30 workers were added to finish the job. After completing the project: were they behind schedule, right on schedule or before schedule?

Feb 14, 2021

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At  the  end  of 90 days,   90 /200   = 9/20  of  the job was finished

Then 10 workers were fired  so,  20 remain

Notice  that   if  30  workers  can finish the job  in  200 days, then each day  1  worker  can complete  1 / (30 * 200)  =    1/6000  of the job

So  20 workers in one day  can complete  20/6000 = 1/300 of  the job....so in  30 days,  they  can complete  another

30 / 300   =  1/10   of the  job  = 2/20  of the job

So before  the last  30  workers  were  hired     9/20  + 2/20  = 11/20  of the job is  complete   and 9/20  is left

So....20 + 30   =  50 workers  complete  the job

Every  day     50 /6000  =   1/120  more of  the job is now finished

So   the  number  of  days  it  takes to  complete  this is

Part  that remains  / Part  completed each day  =

(9/20 ) / ( 1/120)  =  120 ( 9)  /20   =  54 days

So....the total number  of  days    = 90  + 30   + 54  =  174  days.....so....ahead of schedule

Feb 14, 2021