SOLUTION: A and B do a job in 12 days . A did for 8 days then rest job was done by B in 20 days. Find individually A and B can do in how many days.

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Question 925250: A and B do a job in 12 days . A did for 8 days then rest job was done by B in 20 days. Find individually A and B can do in how many days.
Found 2 solutions by stanbon, filmi101:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A and B do a job in 12 days . A did for 8 days then rest job was done by B in 20 days. Find individually A and B can do in how many days.
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Together rate:: 1/12 job/day
A's rate:: 1/a job/day
B's rate:: 1/b job/day
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Equations:
1/a + 1/b = 1/12
3(1/a) + 20(1/b) = 1
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Modify::
12b + 12a = ab
3b + 20a = ab
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Modify for elimination::
12b + 12a = ab
12b + 80a = 4ab
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Subtract::
68a = 2ab
b = 34 days (time for B to do the job alone)
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Solve for "a":
1/a + 1/34 = 1/12
1/a = 1/12 - 1/34
1/a = (34-12)/(12*34)
1/a = 22/(12*34)
a = (12*34)/22
a = 8.55 days (time for A to do the job alone)
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Answer by filmi101(1) About Me  (Show Source):
You can put this solution on YOUR website!
1/a + 1/b = 1/12
8/a+ 20/b = 1
or we can write the equation as
12a+12b = ab
8a+ 20b = an
solving the equation we get a= 36 b= 18