SOLUTION: 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%?

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.,

RELATED QUESTIONS
12 workers can do a piece of work in 16 days if 12 more workers are added in how many... (answered by Cromlix)

If 9 workers complete the work in 10 days how many workers will complete the same work in (answered by josgarithmetic,josmiceli)

16 workers can complete a piece of work in 30 days.After working for 10 days, 4 more... (answered by richwmiller,ikleyn)

If 10 workers do a certain work in 16 days, than in how many days the same work will be... (answered by josgarithmetic)

In Ngomongo village a piece of work can be completed by 45 workers in 10 days .They work... (answered by srinivas.g,macston,josmiceli,MathTherapy)

if 3 workers can finish painting a house in 2 days, how many days will it take 6 workers (answered by josgarithmetic,josmiceli,ikleyn)

Hi 5 workers complete a job in 6 days. After 2 days, 3 workers left. how many more days (answered by Theo)

it took 4 workers 9 days to complete a renovation work.how many workers would it take to... (answered by josgarithmetic)

30 workers complete a work in 15 days and 36 workers to complete same work in how many... (answered by chibisan)