Question 725505
 it takes shawn 12 more hours to paint a house than Michelle. together it takes them 14.4 hours to complete the work. how long would it take shawn to paint the house by himself?
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Shawn's rate = 1/(12+x) job/hr
Together rate = 1/14.4 job/hr
Michelle rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/(12+x) + 1/x = 1/14.4
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[(x+12+x)]/[12x+x^2] = 1/14.4
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[2x+12)/(x^2+12x) = 1/14.4
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14.4(2x+12) = x^2+12x
28.8x + 172.8 = x^2+12x
x^2 -16.8x -172.8 = 0
x = 24 hrs (time for Michelle to do the job alone)
x+12 = 36 hs (time for Shawn to do the job alone)
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Cheers,
Stan H.
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