Question 132056
Phil can paint the garage in 12 hours. That means that each hour he does 1/12 of the job.
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Rick can paint the garage in 10 hours. That means that each hour he does 1/10 of the garage.
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If they work together for 3 hours, Phil does 3 times 1/12 of the garage so he does 3/12 or 1/4 of
the garage or in decimals 0.25 of the garage. 
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At the same time Rick who does 1/10 of the garage every hour does 3/10 of the garage in the
3 hours and in decimals this is 0.30 of the garage.
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So in three hours of working together, their combine progress is 0.25 + 0.30 = 0.55
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This means that of the entire garage they have done 0.55 of it. So there is 0.45 of it left
(1 - 0.55 = 0.45).
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At this point Phil quits and Rick presses on by himself. Since he does 1/10 of the garage every
hour and there are 4.5 tenths of the garage left, it will take Rick 4.5 hours more to 
complete the garage.
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You can get that from the equation:
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1/10 * T = 0.45
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where T represents the time that Rick needs to complete the job after Phil goes on strike.
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Multiply both sides of this equation by 10 and it becomes:
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T = 4.5 hours
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Hope this helps you to understand the problem and enables you to see your way through it in
a logical fashion.  The whole trick to this method begins by recognizing that if a person can
do the entire thing by him/herself in x hours, then each hour (s)he does 1/x of the job.
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