SOLUTION: Every week Naomi stuffs 1000 envelopes. If she does the job by herself it takes 6 hours. If Jill helps it takes 5 1/2 hours. How long would it take Jill to do the job by herself?
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Question 151891: Every week Naomi stuffs 1000 envelopes. If she does the job by herself it takes 6 hours. If Jill helps it takes 5 1/2 hours. How long would it take Jill to do the job by herself?
Please help me understand how to do the equation. Thank you Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Every week Naomi stuffs 1000 envelopes. If she does the job by herself it takes 6 hours. If Jill helps it takes 5 1/2 hours. How long would it take Jill to do the job by herself?
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Let x = time required if Jill does it by herself
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Let the completed job = 1 (represents the stuffing of 1000 envelopes)
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We want to find out what fraction of 1, each person does
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we know that Naomi can complete the job in 6 hours
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Therefore in 5.5 hrs she would complete of the job
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Jill would complete of the job
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The two fractions have to add up to 1 (the completed job)
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With this in mind, we can write an equation and solve for x: + = 1
Get rid of the denominators by multiplying the equation by 6x
6x* + 6x* = 6x(1)
Cancel out the denominators and we have:
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5.5x + 6(5.5) = 6x
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5.5x + 33 = 6x
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33 = 6x - 5.5x
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33 = .5x
x =
x = 66 hrs for Jill working alone (obviously, Jill is not much help)
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It is easy to check this with a calc:
enter (5.5/6) + (5.5/66) = 1
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