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a house three times faster

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a house three times faster

by sanju09 » Tue Nov 15, 2011 3:35 am
Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 24 hours to paint a house, then how many hours would it take Bea to paint a house alone?
(A) 28
(B) 30
(C) 32
(D) 36
(E) 40
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by Anurag@Gurome » Tue Nov 15, 2011 3:37 am
sanju09 wrote:Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 24 hours to paint a house, then how many hours would it take Bea to paint a house alone?
(A) 28
(B) 30
(C) 32
(D) 36
(E) 40
Let Alice takes x hours to paint a house.
Then Bea takes x/3 hours to paint the house.
1 hour work of Alice = 1/x
1 hour work of Bea = 3/x
(1/x) + (3/x) = 1/24 implies x = 96 hrs, that is Alice takes 96 hrs to paint the house, which Bea could have painted in 96/3 = 32 hrs

The correct answer is C.
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