SOLUTION: Suppose that Helena and Corrine can clean their entire house in 7 hours, while their little brother, William, just by being around, can completely mess it up in only 2 hours. If He

Algebra ->  Proportions -> SOLUTION: Suppose that Helena and Corrine can clean their entire house in 7 hours, while their little brother, William, just by being around, can completely mess it up in only 2 hours. If He      Log On


   

Question 956520: Suppose that Helena and Corrine can clean their entire house in 7 hours, while their little brother, William, just by being around, can completely mess it up in only 2 hours. If Helena and Corrine clean the house while William is at his grandma’s house. How long will it take for the house to be in shambles again if Helena and Corrine clean the house again the moment William returns to their house?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Their rate of cleaning:
[ 1 house cleaned ] / [ 7 hrs ]
+1%2F7+
William's rate of messing it up:
[ 1 house messed up ] / [ 2 hrs ]
+-1%2F2+
( the minus sign is needed because this
is the opposite of cleaning the house )
------------------------------------
+1%2Ft+ = rate of getting messed up
+1%2F7+-+1%2F2+=+1%2Ft+
Multiply both sides by +14t+
+2t+-+7t+=+14+
+-5t+=+14+
+t+=+-2.8+
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In 2.8 hrs, the house is messed up again