SOLUTION: One painter takes 6 hours longer to paint a room than does a second painter. Working together, they can paint the room in 4 hours. How long wouold it take each painter working al

Question 182671: One painter takes 6 hours longer to paint a room than does a second painter. Working together, they can paint the room in 4 hours. How long wouold it take each painter working alone to paint the room?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One painter takes 6 hours longer to paint a room than does a second painter. Working together, they can paint the room in 4 hours. How long wouold it take each painter working alone to paint the room?
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2nd painter DATA:
time = x hr/job ; rate = 1/x job/hr
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1st painter DATA:
time = (x+6) hr/job ; rate = 1/(x+6) job/hr
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Together DATA:
time = 4 hr/job ; rate = 1/4 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x+6) = 1/4
Multiply thru by 4x(x+6) to get:
4(x+6) + 4x = x(x+6)
4x + 24 + 4x = x^2 + 6x
x^2 -2x - 24 = 0
(x-6)(x+4) = 0
Positive solution:
x = 6 hrs (time for 2nd painter to do the job alone)
x+6= 12 hrs (time for the 1st to do the job alone)
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Cheers,
Stan H.
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