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Question 38229: It takes Chris 1 1/2 times as long to clean the kitchen as Allison. It takes Allison 1 2/3 times as long to clean the kitchen as Barry. If Chris, Allison and Barry work together, they can clean the kitchen in 3 hours. How long would it take Chris to clean the kitchen alone? Any assistance would be greatly appreciated!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! It takes Chris 1 1/2 times as long to clean the kitchen as Allison. It takes Allison 1 2/3 times as long to clean the kitchen as Barry. If Chris, Allison and Barry work together, they can clean the kitchen in 3 hours. How long would it take Chris to clean the kitchen alone? Any assistance would be greatly appreciated!
Let Barry's time be "x" hrs. His rate is 1/x job/hr.
Then Allison's time is (5/3)x. Her rate is 3/5x job/hr.
And Chris's time is (3/2)(5/3)x=(5/2)x hrs. His rate is 2/5x job/hr.
Together their time is 3 hrs. Their combined rate is 1/3 job/hr.
EQUATION:
Barry rate + Allison rate + Chris rate = 1/3 job/hr
1/x + 3/5x + 2/5x = 1/3
Multiply thru by 15x to get:
15 +9 + 6 =5x
30=5x
x=6
Chris would take (5/2)6 = 15 hrs.
Cheers,
Stan H.
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