SOLUTION: It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 18 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work toget

Question 850050: It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 18 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to finish painting the fence?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 18 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to finish painting the fence?
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Ralph rate:: 1/14 job/hr
Lisa rate::: 1/18 job/hr
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Together rate = (1/14)+(1/18) = (32/(14*18)) = 8/(7*9) = 8/63 job/hr
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in 30 minutes Ralph does (1/14)/2 = 1/28 of the job(
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To finish the job Ralph and Lisa work together for "x" hours:
x(8/63) = 27/28
x = (27/28)/(8/63) = (27*63)/(28*8) = 7.59 hrs = 7 hrs 36 min
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Cheers,
Stan H.
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