SOLUTION: A and B working together can finish a certain job in 20/3 hours. They start the work together but after 3 hours, A became ill and B continuing the work alone finished it in 33/4 ho

Question 685734: A and B working together can finish a certain job in 20/3 hours. They start the work together but after 3 hours, A became ill and B continuing the work alone finished it in 33/4 hours. How long would it take each working alone to do the job.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A and B working together can finish a certain job in 20/3 hours. They start the work together but after 3 hours, A became ill and B continuing the work alone finished it in 33/4 hours. How long would it take each working alone to do the job.
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Let a and b be their respective rates:
Equations:
a + b = (3/20) job/hr
3a + (3+(33/4))b = 1 job/hr
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Rearrange:
3a + 3b = (9/20)
3a + (45/4)b = 1
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Subtract and solve for "b":
(33/4)b = 11/20
b = (11/20)(4/33) = (1/15)
B would take 15 hours to do the job alone
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Solve for "a" using a + b = 3/20
a + 1/15 = 3/20
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a = (3/20)-(1/15)
a = (9-4)/60 = 1/12
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A would take 12 hours to do the job alone
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Cheers,
Stan H.
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