Question 149944
Working together, a painter and the painter's apprentice can paint a room in 
4 hours.
Time = 4 hrs/job ; Rate = 1/4 job/hr.
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 Working alone, the apprentice requires 7 more hours to paint the room than the painter requires working alone.
Painter's DATA:
Time = x hrs/job ;  Rate = 1/x job/hr.
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Apprentice DATA: 
Time = (x+7) hr/job  ; Rate = 1/(x+7) job/hr
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How long does it take the painter, working alone, to paint the room?
Please round your answer to one decimal place. 
EQUATION:
rate + rate = together rate
1/x + 1/(x+7) = 1/4

Multiply thru by 4x(x+7) to get:
4(x+7) + 4x = x(x+7)
4x+28 + 4x = x^2+7x
x^2 -x -28 = 0
x = [1 +- sqrt(1-4*-28)]/2
Positive solution:
x = [1 + sqrt(29)]/2
x = 3.2 hrs (Painter's time to do the job)
x+7 = 10.2 hrs (Apprentices's time to do the job)
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Cheers,
Stan H.