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?

Question 188612: 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?
I would like you to do this problem step by step and explain because it's hard for me to understand.Thanks A lot!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
------------------------
Faster maid DATA:
time = x hr/job ; rate = 1/x job/jhr
-------------------------
Slower maid DATA:
time = 3x hr/job ; rate = 1/3x job/hr
---------------------------
Together DATA:
time = 3 hr/job ; rate = 1/3 job/hr
-----------------------------------------
Equation:
rate + rate = together rate
1/x + 1/3x = 1/3
-----
Multiply thru by 3x to get:
3 + 1 = x
x = 4 hrs (time for the faster maid to do the job)
============================
Cheers,
Stan H.
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