SOLUTION: working along henry takes 9 hours longer than mary to clean the carpets in the entire office working together they clean the carpets in 6 hours how long wound it take mary to cle

Algebra ->  Rate-of-work-word-problems -> SOLUTION: working along henry takes 9 hours longer than mary to clean the carpets in the entire office working together they clean the carpets in 6 hours how long wound it take mary to cle      Log On


   

Question 996949: working along henry takes 9 hours longer than mary to clean the carpets in the entire office working together they clean the carpets in 6 hours how long wound it take mary to clean the office carpets if henry were not there to help?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get
their rate working together
Let +t+ = Mary's time to clean the carpets
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Mary's rate working alone:
[ 1 office ] / [ t hrs ]
Henry's rate:
[ 1 office ] / [ t + 9 hrs ]
Working together:
[ 1 ofice ] / [ 6 hrs ]
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+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+
Multiply both sides by +6t%2A%28+t%2B9+%29+
+6%2A%28+t%2B9+%29+%2B+6t+=+t%2A%28+t%2B9+%29+
+6t+%2B+54+%2B+6t+=+t%5E2+%2B+9t+
+t%5E2+-+3t+-+54+=+0+
+%28+t+-+9+%29%2A%28+t+%2B+6+%29+=+0+ ( by looking at it )
+t+=+9+ ( can't use negative time )
It takes Mary 9 hrs working alone
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check:
+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+
+1%2F9+%2B+1%2F%289%2B9+%29+=+1%2F6+
+2%2F18+%2B+1%2F18+=+3%2F18+
+3%2F18+=+3%2F18+
OK