Work Problem

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Work Problem

by mrclassact2005 » Thu Oct 18, 2012 6:05 pm
If Art and Rita can do a job in 4 hours when working together at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?

The answer is 12.

Anyone know how you come up with the answer? Please write the way you arrived at the solution for all of us to follow.
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by GMATGuruNY » Mon Oct 22, 2012 5:33 pm
mrclassact2005 wrote:If Art and Rita can do a job in 4 hours when working together at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?
Let the job = 12 units.
Since the time for Art and Rita is 12 hours, their combined rate = w/t = 12/4 = 3 units per hour.
Since the time for Art alone is 6 hours, Art's rate alone = w/t = 12/6 = 2 units per hour.
Thus, Rita's rate alone = (Art and Rita's combined rate) - (Art's rate alone) = 3-2 = 1 unit per hour.
Thus, the time for Rita alone = w/r = 12/1 = 12 hours.
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by bobdylan » Tue Oct 23, 2012 12:47 pm
First add individual rates:
Art rate + Rita rate= 1/6 + 1/T= T+6/6T.
Then multiply the added rates by the time they worked together= 4T+24=6T = 2T=24 =T=12

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by bobdylan » Tue Oct 23, 2012 12:48 pm
First add individual rates:
Art rate + Rita rate= 1/6 + 1/T= T+6/6T.
Then multiply the added rates by the time they worked together= 4T+24=6T = 2T=24 =T=12