Work Rate Problem

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adsuper7: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri Sep 10, 2010 11:45 pm

by adsuper7 » Sat Oct 15, 2011 9:34 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

C. 32

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Source: Beat The GMAT — Problem Solving | Sat Oct 15, 2011 9:34 am

zooki: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Fri Oct 14, 2011 10:15 amFollowed by: 1 member; Thanked: 4 times

by zooki » Sat Oct 15, 2011 9:39 am

1/Tb + i/Ta= 1/24

Tb=3Ta
Tb=hours it takes Bea to Pain the house
Ta=hours it takes Alice to Pain the house

Solving for Ta= 32

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sat Oct 15, 2011 9:42 am

1/B + 1/3B = 1/24

B = 32.B

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sat Oct 15, 2011 12:15 pm

adsuper7 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 will it take Bea to paint a house alone?

A. 28
B. 30
C. 32
D. 36
E. 40

C. 32

Let efficiency of Alice be 1 unit/hr

So efficiency of Bea is 3 units/hr

Working together their efficiency adds up....

So total efficiency is 4 units/hr, the complete the job in 24 hrs...

So total work = 24 * 4 ( Work = efficiency*time)

work =96 units...

Now time taken by Bea is Work / bea's efficiency => 96/3 = 32 hrs...

Abhishek

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Oct 15, 2011 1:40 pm

adsuper7 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 will it take Bea to paint a house alone?

A. 28
B. 30
C. 32
D. 36
E. 40

C. 32

We can plug in the answers, which represent the time for Bea to paint the house alone.

Answer choice C: 32 hours.
Let the house = 96 units.
Rate for Bea = w/t = 96/32 = 3 units per hour.
Rate for Alice and Bea together = w/t = 96/24 = 4 units per hour.
Rate for Alice alone = rate for Alice and Bea together - rate for Bea alone = 4-3 = 1 unit per hour.
Rate for Bea/rate for Alice = 3/1 = 3.
Success!

The correct answer is C.

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Mon Oct 17, 2011 9:22 pm

Agree with Mitch. We can solve this by directly putting the values from the options.

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Be at the gmat: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Oct 20, 2011 2:04 am

by Be at the gmat » Thu Oct 20, 2011 2:08 am

Since Bea can paint a house 3 times faster than Alice as opposed to 3 times as fast as Alice, she would do four times as much work every hour.
solve 1/A + 1/4A = 1/24

or
time taken by Bea working alone = 24X5/4 = 30 days

Answer should be option B

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rohit_gmat: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

by rohit_gmat » Thu Oct 20, 2011 3:06 am

let house (work) = 24 units

(rate) B = 3A
& combined rate 4A can do 24 units in 24 hours ... meaning 4A = 1 unit/hr
A = 1/4 unit/hr
B = 3/4 unit/hr

time for B alone = 24 units / (3/4 units/hr) = 32 hours

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