SOLUTION: It takes Shawn 6 more hours to stain a deck than Michelle. Together it takes them 1.6 hours to complete the work. How long does Shawn take to stain the deck by himself?

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Question 676202: It takes Shawn 6 more hours to stain a deck than Michelle. Together it takes them 1.6 hours to complete the work. How long does Shawn take to stain the deck by himself?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Michelle's time in hrs to stain deck
+t+%2B+6+ = Shawn's time in hrs to stain deck
Add their rates of working to get rate working together
( 1 deck stained ) / ( Shawn's time ) + ( 1 deck stained ) / ( Michelle's time ) = rate working together
+1+%2F+%28+t+%2B+6+%29+%2B+1%2Ft+=+1+%2F+1.6+
Multiply both sides by +1.6%2A%28+t+%2B+6+%29%2At+
+1.6t+%2B+%28+t+%2B+6+%29%2A1.6+=+t%2A%28+t+%2B+1.6+%29+
+1.6t+%2B+1.6t+%2B+9.6+=+t%5E2+%2B+1.6t+
+1.6t+%2B+9.6+=+t%5E2+
+t%5E2+-+1.6t+-+9.6+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-1.6+
+c+=+-9.6+
+t+=+%28-%28-1.6%29+%2B-+sqrt%28+%28-1.6%29%5E2+-+4%2A1%2A%28-9.6%29+%29%29+%2F+%282%2A1%29+
+t+=+%28+1.6+%2B-+sqrt%28+2.56+%2B+38.4+%29%29+%2F+2+
+t+=+%28+1.6+%2B-+sqrt%28+40.96+%29%29+%2F+2+
+t+=+%28+1.6+%2B+6.4%29+%2F+2+ ( ignore the negative square root )
+t+=+8%2F2+
+t+=+4+
+t+%2B+6+ = Shawn's time, so
+t+%2B+6+=+10+
Shawn takes 10 hrs to stain deck by himself