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Question 425458: Pls help: "it takes 6 people 10 hours to complete a certain job. How many hours will it take 10 people working at the same rate, to complete 2/3 of the same job"
Found 2 solutions by robertb, Edwin McCravy:
Answer by robertb(5830)   (Show Source):
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! Pls help: "it takes 6 people 10 hours to complete a certain job. How many hours will it take 10 people working at the same rate, to complete 2/3 of the same job"
One way to do it is that this fraction must stay constant:
WORKERS × TIME WORKERS × TIME
—————————————— = ——————————————
JOBS JOBS
6 × 10 10 × T
—————— = ————————
1 2/3
60 10T
——— = —————
1 2/3
10T = 60(2/3)
10T = 40
T = 4
4 hours.
OR
This principle:
1. If you MULTIPLY the number of people by N, you must DIVIDE the
number of hours by that same number N.
2. If you DIVIDE the number of people by N, you must MULTIPLY the
number of hours by that same number N.
3. If you have only a fraction of a job, take that fraction of the
hours.
Start with:
"It takes 6 people 10 hours to complete the job."
DIVIDE the 6 people by 3, getting 2, and MULTIPLY the 10 hours by 3, getting 30.
"It takes 2 people 30 hours to complete the job."
MULTIPLY the 2 people by 5, getting 10, and DIVIDE the 30 hours by 5, getting 6.
"It takes 10 people 6 hours to complete the job."
Take the fraction of hours that you take of the job:
Therefore it will take 10 people only 2/3 as long or 4 hours to complete 2/3
of the job.
Edwin
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