Work Problem

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vladmire: Master | Next Rank: 500 Posts; Posts: 132; Joined: Tue Oct 07, 2008 4:59 pm; Thanked: 4 times

by vladmire » Wed Feb 18, 2009 6:30 am

Whats the next step
I know the formula is 1/t1 + 1/t2 = 1/t t=total hours or days I guess of both people working.

Clarissa and Shawna working together can paint the exterior of a house in 6 days. Clarissa by herself can complete this job in 5 days less than Shawna. How long will it take Clarissa to complete the job by herself?

A.16 days
B. 17.5 days
C. 19 days
D. 18.5 days
E. 20 days

C + S = 6 right and S-5 = C

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Source: Beat The GMAT — Problem Solving | Wed Feb 18, 2009 6:30 am

billzhao: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Feb 02, 2009 6:36 am; Thanked: 10 times

Re: Work Problem

by billzhao » Wed Feb 18, 2009 6:47 am

vladmire wrote:Whats the next step
I know the formula is 1/t1 + 1/t2 = 1/t t=total hours or days I guess of both people working.

Clarissa and Shawna working together can paint the exterior of a house in 6 days. Clarissa by herself can complete this job in 5 days less than Shawna. How long will it take Clarissa to complete the job by herself?

A.16 days
B. 17.5 days
C. 19 days
D. 18.5 days
E. 20 days

C + S = 6 right and S-5 = C

Assume the rate of Clarissa is rc and that of Shawna is rs:
From the question, we know that:

(rc+rs)=1/6...........................(1)
1/rc+5=1/rs..........................(2)

From (1) and (2), we can solve for rc.
rc=1/10, rs=1/15

So tc=10 hours, Clarissa needs 10 hours to complete the job by herself and Shawna needs 15 hours to complete the job by herself.

Yiliang

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vladmire: Master | Next Rank: 500 Posts; Posts: 132; Joined: Tue Oct 07, 2008 4:59 pm; Thanked: 4 times

by vladmire » Wed Feb 18, 2009 7:07 am

Clarissa needs 10 hours to complete the job by herself and Shawna needs 15 hours to complete the job by herself

In this case needs only Carissa at 10hrs. and Shawna at 15hrs to paint the house alone. Would put them working together to complete the painting of the house in 1 day and a hour, but the question stem says together they would complete the painting in 6 days or 144 hours.

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x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

Re: Work Problem

by x2suresh » Wed Feb 18, 2009 7:44 am

vladmire wrote:Whats the next step
I know the formula is 1/t1 + 1/t2 = 1/t t=total hours or days I guess of both people working.

Clarissa and Shawna working together can paint the exterior of a house in 6 days. Clarissa by herself can complete this job in 5 days less than Shawna. How long will it take Clarissa to complete the job by herself?

A.16 days
B. 17.5 days
C. 19 days
D. 18.5 days
E. 20 days

C + S = 6 right and S-5 = C

Rc +Rs = Rsc

1/t-5 + 1/t = 1/6

6(2t-5)= t^2-5t
t^2-17t+30 = 0

t=15 or 2 (2 is ruled out.)

C can complete job in 10 days. S can complete job in 15 days.

I don't see the answer..

What is the source?

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