SOLUTION: a person can do a piece of work in 12 days. after working alone or 4 days.he hires a helper and both them together complete the task for 6 days.how long would it have taken for the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a person can do a piece of work in 12 days. after working alone or 4 days.he hires a helper and both them together complete the task for 6 days.how long would it have taken for the      Log On


   

Question 764331: a person can do a piece of work in 12 days. after working alone or 4 days.he hires a helper and both them together complete the task for 6 days.how long would it have taken for the helper to alone to complete a given task?
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Found 2 solutions by solver91311, josgarithmetic:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Why did you ask the same question twice?

John

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My calculator said it, I believe it, that settles it
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Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
The work rate for "a person" is 1/12 jobs per day.

Amount of job to be done with a person and his helper AFTER 4 days is
1-%281%2F12%29%2A4 jobs
1-1%2F3
2%2F3 job.

The portion of the job was done in 6 days but we do not yet know the combined work rates:
R%2A6=2%2F3 where R is the work rate of the helper PLUS a person, in jobs per day.
R=2%2F%283%2A6%29
R=1%2F9 jobs per day

The work rates of a person AND helper are added by arithmetic addition when they are working together.
Let r= work rate of the help alone:
1%2F12%2Br=1%2F9
r=1%2F9-1%2F12
r=4%2F36-3%2F36
highlight%28r=1%2F36%29 jobs per day
That is the same as meaning 36 days to do one job.