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?
+130071 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
