it takes Alice and Bea 24

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Sep 14, 2010 3:59 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 will it take Bea to paint a house alone?
(A) 28
(B) 30
(C) 32
(D) 36
(E) 40

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Source: Beat The GMAT — Problem Solving | Tue Sep 14, 2010 3:59 am

kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Tue Sep 14, 2010 4:28 am

Let time taken by Alice = 3x, then time taken by Bea = x

Let their time taken together = T

1/x + 1/3x = 1/T

=> t = 3x/4 = 24 => x = 32 = Time taken by Bea

(C) ?

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Tue Sep 14, 2010 4:31 am

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 [spoiler](C)[/spoiler].

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ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

by ankur.agrawal » Tue Sep 14, 2010 4:34 am

Alice and Bea 24 hours to paint a house: means that in 1 hr they will complete 1/24th of the work.

Bea can paint a house three times faster than Alice can paint a house: Means that if alice takes t time to complete a work Bea will take (1/3) t to complete same work.

Alice - takes t time to complete 1 work - in 1 hr it will do - 1/t work

Bea- takes (1/3)t time to complete the same work- in 1 hr it will do- 1/(t/3) work= 3/t work

1/t+ 3/t = 1/24

Solving this we get t=96. So bea will take 1/3 *96 = 32 hrs to do the work.

So C.

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