SOLUTION: One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?

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Question 248629: One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Faster maid's rate of working + slower maids rate = rate working together
Let x = slower maids rate of working in (1 house cleaned)/(time to clean it)
then, Faster maid's rate = 3x
x+%2B+3x+=+1%2F3 (note: 1/3 is: (1 house/(3 hours))
3x+%2B+9x+=+1
12x+=+1
x+=+1%2F12
The slower maid can clean 1 house in 12 hours
The faster maid's rate is:
3x+=+3%2A%281%2F12%29+=+3%2F12
3%2F12+=+1%2F4
The faster maid can clean the house in 4 hours