Question 1080759: 16 workers complete their work in 38 days. In how many days will it take if 5 of the workers increase their work load by 60%?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! p*r*t = q
p = numnber of people
r = rate that each person works
t = time
q = quantity of work produced.
in your problem, you start with 16 * r * 38 = 1
p = 16
r = rate that each person works per day
t = 38 days
q = 1 job
solve for r in this equation to get r = 1/(16 * 38) = 1/608
each worker completes 1/608 of the job per day.
16 * 1/608 * 38 = 1 job completed.
5 of the workers increases their workload by 60%
1.6 * 1/608 = 1.6/608
now you have 11 of the workers completing 1/608 of the job per day and you have 5 of the workers completing 1.6/608 of the job per day.
you want to solve for time.
when they work together, the worker's rates are additive.
p * r * t = q becomes:
(11 * 1/608) + 5 * (1.6/608) * t = 1
solve for t to get t = 1 / (11 * 1/608) + 5 * 1.6/608) = 32
the job will be completed in 32 days
the 5 workers will complete 5 * 1.6/608 * 32 = .4210526316 of the job in 32 days.
the 11 workers will comlete 11 * 1/608 * 32 = .5789473684 of the job in 32 days.
combine their efforts and the whole job is completed in 32 days.,
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