SOLUTION: it takes shawn 9 more hour to paint a house than michelle. together it takes them 10.8 hours to complete work. How long would it take Shawn to paint the house by himself.

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Question 945590: it takes shawn 9 more hour to paint a house than michelle. together it takes them 10.8 hours to complete work. How long would it take Shawn to paint the house by himself.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Michelle's time to paint a house in hours
+t+%2B+9+ = Shawn's time to paint a house in hours
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( 1 house ) / ( t hours ) = Michelle's rate of painting
( 1 house ) / ( t + 9 hours ) = Shawn's rate of painting
( 1 house ) / ( 10.8 hours ) = their rate painting together
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Add their rates of painting to get their rate painting together
+1%2Ft+%2B+1+%2F+%28+t+%2B+9+%29+=+1+%2F+10.8+
Multiply both sides by +10.8%2At%2A%28+t%2B+9+%29+
+10.8%2A%28+t+%2B+9+%29+%2B+10.8t+=+t%2A%28+t+%2B+9+%29+
+10.8t+%2B+97.2+%2B+10.8t+=+t%5E2+%2B+9t+
+t%5E2+%2B+9t+-+21.6t+-+97.2+=+0+
+t%5E2+-+12.6t+-+97.2+=+0+
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Use the quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b++-12.6+
+c+=+-97.2+

+t+=+%28+12.6+%2B-+sqrt%28+158.76+%2B+388.8+%29%29+%2F+2+
+t+=+%28+12.6+%2B-+sqrt%28+547.56+%29%29+%2F+2+
+t+=+%28+12.6+%2B+23.4+%29+%2F+2+
+t+=+36%2F2+ ( can't use the negative square root )
+t+=+18+
+t+%2B+9+=+27+
Shawn takes 27 hrs to paint the house by himself
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check:
+1%2Ft+%2B+1+%2F+%28+t+%2B+9+%29+=+1+%2F+10.8+
+1%2F18+%2B+1+%2F+27+=+1+%2F+10.8+
Divide both sides by +9+
+1%2F2+%2B+1%2F3+=+1%2F1.2+
Multiply both sides by +1%2F10+
+1%2F20+%2B+1%2F30+=+1%2F12+
Multiply both sides by +60+
+3+%2B+2+=+5+
OK