SOLUTION: Workers A and B can complete a particular job if they work together for 12 days. If A works alone for 20 days and then B completes the job alone in 6 more days, how long does it

Question 927797: Workers A and B can complete a particular job if they work together for 12 days. If A
works alone for 20 days and then B completes the job alone in 6 more days, how long does it
take each worker to do the job?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Workers A and B can complete a particular job if they work together for 12 days. If A
works alone for 20 days and then B completes the job alone in 6 more days, how long does it
take each worker to do the job?
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Together rate: 1/12 job/day
A's rate:: 1/a job/day
B's rate:: 1/b job/day
-------
Equations:
1/a + 1/b = 1/12
20(1/a) + 6(1/b) = 1 job
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Substitute for 1/a and solve for 1/b::
20(1/12-1/b) + 6(1/b) = 1
(5/3) - 20(1/b) + 6(1/b) = 1
-----
-14(1/b) = -2/3
(1/b = (2/3)/14 = 1/21
b = 21 days (time for "B" to do the job alone)
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Solve for 1/a::
1/a + 1/21 = 1/12
1/a = (1/12)-(1/21)
1/a = (21-12)/(12*21)
1/a = 9/(12*21) = 1/28
a = 28 days (time for "A" to do the job alone)
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Cheers,
Stan H.
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