SOLUTION: Together, Andy and Ben can re-roof a certain house in six days. When Ben works alone, it takes him 9 days longer than when Andy works by himself. How long does it take each person

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Together, Andy and Ben can re-roof a certain house in six days. When Ben works alone, it takes him 9 days longer than when Andy works by himself. How long does it take each person       Log On


   

Question 1097168: Together, Andy and Ben can re-roof a certain house in six days. When Ben works alone, it takes him 9 days longer than when Andy works by himself. How long does it take each person to re-roof the same house independently?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Andy's time in days to re-roof a house
Andy's rate of working is:
[ 1 house re-roofed ] / [ t days ]
Ben's rate of working is:
[ 1 house re-roofed ] / [ t + 9 days ]
Their rate working together:
[ 1 house re-roofed ] / [ 6 days ]
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Add their individual rates to get their rate working together
+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+
Multiply both sides by +6t%2A%28+t+%2B+9+%29+
+6%2A%28+t+%2B+9+%29+%2B+6t+=+t%2A%28+t+%2B+9+%29+
+6t+%2B+54+%2B+6t+=+t%5E2+%2B+9t+
+t%5E2+-+3t+-+54+=+0+
+%28+t+%2B+6+%29%2A%28+t+-+9+%29+=+0+ by looking at it
+t+=+9+ ( can't use the negative solution )
and
+t+%2B+9+=+18+
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Andy takes 9 days working alone
Ben takes 18 days working alone
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check:
+1%2Ft+%2B+1%2F%28t%2B9%29+=+1%2F6+
+1%2F9+%2B+1%2F18+=+1%2F6+
+2%2F18+%2B+1%2F18+=+3%2F18+
+3%2F18+=+3%2F18+
OK