SOLUTION: Three brothers, Philip, Rafael and Brian live in a house. Philip can clean the hoouse twice times as fast as Brian. Rafael can clean the house in 8 hours. All three together, can c

Question 186461: Three brothers, Philip, Rafael and Brian live in a house. Philip can clean the hoouse twice times as fast as Brian. Rafael can clean the house in 8 hours. All three together, can clean the house in 2 hours. How long would it take Brian to clean the house.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Three brothers, Philip, Rafael and Brian live in a house.
Philip can clean the house twice times as fast as Brian.
Rafael can clean the house in 8 hours.
All three together, can clean the house in 2 hours.
How long would it take Brian to clean the house.
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Let Brian time = 2x hr/job ; rate = 1/(2x) job/hr.
------------
Then Philip time = x hr/job ; rate = 1/x job/hr.
-----------
Rafael time = 8 hrs/job ; rate = 1/8 job/hr.
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Together time = 2 hrs/job ; rate = 1/2 job/hr
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Equation:
rate + rate + rate = together rate
1/2x + 1/x + 1/8 = 1/2
Multiply thru by 8x to get:
4 + 8 + x = 4x
3x = 12
x = 4 hrs (Philip time to do the job alone)
2x= 8 hrs (Brian time to do the job alone)
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Cheers,
Stan H.
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