Question 1209086: Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job 6 days earlier. If the job needs to be completed 32 days earlier, how many additional workers should be hired?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52767)   (Show Source):
You can put this solution on YOUR website! .
Five workers have been hired to complete a job.
If one additional worker is hired, they could complete the job 6 days earlier.
If the job needs to be completed 32 days earlier, how many additional workers should be hired?
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Solve it step by step.
Step 1 - determine the number of days needed for 5 workers
to complete the job.
Let d be the number of days for 5 workers to complete the job.
Then the entire job is 5d worker-days.
6 workers could complete the job in (d-6) days.
Hence, from this perspective, the entire work is 6*(d-6) worker-days.
It gives us this equation
5d = 6(d-6),
from which we get
5d = 6d - 36 ---> 36 = 6d - 5d ---> 36 = d.
Hence, 5 workers need 36 days to complete the job, and the entire job is 5*36 = 180 worker-days.
Step 2 - determine the number of workers needed
to complete the job in 32 days earlier.
The question wants the job be complete in 36-32 = 4 days.
It requires 180/4 = 45 workers.
Step 3 - determine the number of additional workers
to be hired.
The number of additional workers is 45 - 5 = 40.
ANSWER. 40 additional workers should be hired to complete the job in 32 days earlier.
Solved.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
Answer: 40 extra workers
Explanation
Let's say the job is to move 9000 boxes.
I'm picking this value since it's a multiple of 5 and 6.
You can change 9000 to anything else you want to get the same answer at the end.
If there are 5 workers, then each worker handles 9000/5 = 1800 boxes.
Each worker has a unit rate of 1800/x boxes per day.
x is the number of days to finish the job with 5 workers.
rate = amountDone/time
When there are 6 workers, each person now gets 9000/6 = 1500 boxes.
The unit rate per person is 1500/(x-6) where the x-6 refers to finishing the job 6 days early compared to the previous scenario.
If we assume each worker has the same unit rate, then we get this equation
1800/x = 1500/(x-6)
Solving it leads to x = 36.
I'll let the student handle the scratch work.
It takes 36 days for 5 workers to do the job.
It takes 30 days for 6 workers to do the same job.
Each worker moves 50 boxes per day because 1800/36 = 50 or 1500/30 = 50.
n = number of additional workers to hire
n+5 = total number of workers when including the original 5 workers
9000/(n+5) = number of boxes each worker handles
The goal is to finish 32 days early. So instead of taking 36 days it should take 36-32 = 4 days
rate*time = amount done
(50 boxes per day)*(4 days) = 9000/(n+5) boxes
50*4 = 9000/(n+5)
Solving for n leads to n = 40
I'll let the student handle the scratch work.
More practice with a similar question is found here
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