SOLUTION: Sarah takes 3 hours longer to paint a floor than it takes John. When they work together, it takes them 2 hours. How long would each take to do the job alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Sarah takes 3 hours longer to paint a floor than it takes John. When they work together, it takes them 2 hours. How long would each take to do the job alone?      Log On


   

Question 959735: Sarah takes 3 hours longer to paint a floor than it takes John. When they work together, it takes them 2 hours. How long would each take to do the job alone?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Sarah takes 3 hours longer to paint a floor than it takes John.
When they work together, it takes them 2 hours.
How long would each take to do the job alone?
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Sarah DATA:: time = x+3 hrs/job ; rate = 1/(x+3) job/hr
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John DATA:: time = x hrs/job ; rate = 1/x job/hr
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Together DATA:: time = 2 hr/job ; rate = 1/2 job/hr
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Equation:
rate + rate = together rate
1/(x+3) + 1/x = 1/2
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2x + 2(x+3) = x(x+3)
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4x+6 = x^2 + 3x
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x^2 - x - 6 = 0
Factor::
(x-3)(x+2) = 0
x = 3 hrs (time for John to do the job alone)
x+3 = 6 hrs (time for Sarah to do the job alone)
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Cheers,
Stan H.
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