Question 1080759
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.,