In this case the rate is the combination of the three people's rates. Sally cleans at 1/8 of the house per hour. Dad cleans at the rate of 1/6 of the house per hour. Dennis the Menace messes (un-cleans) at the rate of 1/10 of the house per hour. So his rate is subtracted when they work together.

1 = (1/8 + 1/6 - 1/10) * t = (23/120)t so t = 120/23 = 5 and 5/23 hours orabout 5 hours 13 minutes.

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Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Add Sally and Father's rates of cleaning, then
subtract Dennis's rate of messing up.
------------
Sally's rate: ( 1 house cleaned ) / ( 8 hrs )
Father's rate: ( 1 house cleaned ) / ( 6 hrs )
Dennis's rate: ( 1 house messed up ) / ( 10 hrs )
Rate with all 3 together: ( 1 house cleaned ) / ( t hrs )
------------

Multiply both sides by



approximately
It will take 5 hrs and 13 min to clean the house
check:



OK