SOLUTION: Neil can paint a wall in 45 minutes; Scott, in 30 minutes. If neil begins painting the wall and Scott joins in after 15 minutes, how long will it take both to finish the job?

Question 616730: Neil can paint a wall in 45 minutes; Scott, in 30 minutes. If neil begins painting the wall and Scott joins in after 15 minutes, how long will it take both to finish the job?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Neil can paint a wall in 45 minutes
Neil rate = 1/45 job/min
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Scott, in 30 minutes
Scott rate = 1/30 job/min
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If neil begins painting the wall and Scott joins in after 15 minutes, how long will it take both to finish the job?
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Neil finishes 15(1/45) = 1/3 of the job before Scott joins in.
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Together rate = 1/x job/min
Equation:
rate + rate = together rate
1/45 + 1/30 = 1/x
(30x + 45x) = 45*30
75x = 45*30
x = (3/5)30
x = 18 minutes
Together rate is 1/18 job/min
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How long will it take both to finish the job?
Equation
Find time for them to do 2/3 of the job together
t(1/18) = 2/3
x = 18(2/3)
x = 12 minutes
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Cheers,
Stan H.
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