SOLUTION: It takes me 4 less hours to paint a room than my husband would take to paint the same room. If they can paint this size room in 1 ½ hours working together, how long would each of t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes me 4 less hours to paint a room than my husband would take to paint the same room. If they can paint this size room in 1 ½ hours working together, how long would each of t      Log On


   

Question 476353: It takes me 4 less hours to paint a room than my husband would take to paint the same room. If they can paint this size room in 1 ½ hours working together, how long would each of them take to paint the room alone?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
It takes me 4 less hours to paint a room than my husband would take to paint the same room. If they can paint this size room in 1 ½ hours working together, how long would each of them take to paint the room alone?
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Husband DATA:
time = x hrs/job : rate = 1/x job/hr
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"My" DATA:
time = x-4 hrs/job ; rate = 1/(x-4)job/hr
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Together DATA:
time = 3/2 hrs/job ; rate = 1/(3/2) = 2/3 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x-4) = 2/3
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3(x-4) + 3x = 2x(x-4)
6x - 12 = 2x^2-8x
2x^2-14x + 12 = 0
x^2 -7x + 6 = 0
Factor:
(x-6)(x-1) = 0
x = 6 hrs (Husband's time to do the job)
x-4 = 2 hrs (My's time to do the job)
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Cheers,
Stan H.
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