SOLUTION: If one maid can clean a house in 4 hours and another maid can clean a house in 6 hours how long would it take for the both of them to clean the house if they worked together?

Question 347041: If one maid can clean a house in 4 hours and another maid can clean a house in 6 hours how long would it take for the both of them to clean the house if they worked together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time needed for both maids working together to clean the house
Then both maids working together clean at the rate of 1/x house per hour
One maid cleans at the rate of 1/4 house per hour
The other maid cleans at the rate of 1/6 house per hour
Together they clean at the rate of 1/4 + 1/6=3/12 + 2/12=5/12 house per hour
Sooooo our equation to solve is:
5/12=1/x multiply each side by 12x
5x=12 divide each side by 5
x=12/5 hours = 2 2/5 hours or 2 hr 24 min----time needed with both maids working together
CK
In 12/5 hours, first maid cleans (1/4)(12/5)=3/5 of the house
In 12/5 hours, the second maid cleans (1/6)(12/5)=2/5 of the house
3/5 + 2/5=5/5=1 (house that is)
Hope this helps--ptaylor
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