SOLUTION: Ann can paint a house in 15 hours alone, and ann and susann can paint it in 6 hours how long will it take susann to paint it alone???

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Question 153648: Ann can paint a house in 15 hours alone, and ann and susann can paint it in 6 hours how long will it take susann to paint it alone???
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose Susan can paint the house alone in x hours.
So their rates are:
(think of the whole job as 1.)
Ann alone can do 1%2F15 of the whole job per hour.
Susan alone can do 1%2Fx of the whole job per hour.
In 6 hours Ann can do 6%2A%281%2F15%29 of the whole job.
In 6 hours Susan can do 6%2A%281%2Fx%29 of the whole job.
As working jointly both of them can complete the job in 6 hours, we have
6%2A%281%2F15%29%2B6%2A%281%2Fx%29=1
Solving for x, we have
15x%286%2A%281%2F15%29%2B6%2A%281%2Fx%29%29=1%2A15x (multiply both sides by 15x)
15x%2A6%2A%281%2F15%29%2B15x%2A6%2A%281%2Fx%29=1%2A15x
6x%2B90=15x
90=9x
90%2F9=x
10=x
x=10
So it takes Susan 10 hours to paint the house alone