SOLUTION: I'd like someone to show me how to you work out this problem I know the answer I'm just not sure how I got it and I'm trying to help my niece learn it so I'd like to show her how t

Question 363816: I'd like someone to show me how to you work out this problem I know the answer I'm just not sure how I got it and I'm trying to help my niece learn it so I'd like to show her how to work it out. The problem is below
Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel 9 hours. Find out how long it would take Paul to do it alone.
I'll wait to hear from someone,
Thanks
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel 9 hours. Find out how long it would take Paul to do it alone.
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The "trick" is to use the amount of work done per hour, the reciprocal of how many hours it takes. Then you can add the terms.
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Paul & Daniel do 1/4.95 of the job per hour.
Daniel does 1/9 of the job per hour.
Paul takes x hours alone, so
Paul does 1/x of the job per hour.
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1/9 + 1/x = 1/4.95
Multiply thru by 9x
x + 9 = 9x/4.95 = x/0.55
x - x/0.55 = -9
x - 20x/11 = -9
-9x/11 = -9
x = 11 hours
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