SOLUTION: Working together, Alice and Betty can do a certain job in 4 1/3 days. But Alice fell ill after 2 days of working and Betty finished the job continuing to work alone in 6 3/4 more d

Question 352096: Working together, Alice and Betty can do a certain job in 4 1/3 days. But Alice fell ill after 2 days of working and Betty finished the job continuing to work alone in 6 3/4 more days. How long would it take each to do the job if each of them worked alone?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Working together, Alice and Betty can do a certain job in 4 1/3 days. But Alice fell ill after 2 days of working and Betty finished the job continuing to work alone in 6 3/4 more days. How long would it take each to do the job if each of them worked alone?
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Let a and b be Alice and Betty's rate.
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a + b = 1/[4 1/3]
a + b = 1/(13/3) = 3/13
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In 2 days A and B complete 2(3/13) = 6/13 of the job.
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Equation:
time*rate = work done
(Betty time)(Betty rate) = 7/13 of job
(6 3/4)b = 7/13
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(27/4)b = 7/13
b = (4/27)(7/13)
b = 28/351 (Betty's rate when working alone)
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Using a + b = 3/13, solve for "a"
a = 3/13 - 28/351
a = 53/351
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Alice's time alone = 351/53 = 6.62 days
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Betty's time alone = 12.54 days
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Cheers,
Stan H.

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