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Each of two carpenters, A and B, is working to build bookshelves. A,

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Each of two carpenters, A and B, is working to build bookshelves. A, [#permalink]

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New post 17 Mar 2017, 03:09
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Question Stats:

94% (00:38) correct 6% (00:12) wrong based on 77 sessions

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Each of two carpenters, A and B, is working to build bookshelves. A, working alone, can complete the job in 10 hours. If B, working alone, can complete the job in 6 hours, how long will it take A and B working together to complete the job?

A. 15/4 hours
B. 15/2 hours
C. 8 hours
D. 39/4 hours
E. 16 hours

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Re: Each of two carpenters, A and B, is working to build bookshelves. A, [#permalink]

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New post 17 Mar 2017, 12:22
A, working alone, can complete the job in 10 hours --> Rate for A = Total Work/10

B, working alone, can complete the job in 6 hours --> Rate for B = Total Work/6

Combined Rate for A and B = Total Work/10 + Total Work/6

Time taken to complete Total work together:

(Total Work/10 + Total Work/6) * Time = Total Work

Time * (6+10)/60 = 1

Time = 60/16 = 15/4 hrs.

Answer is A. 15/4 hours
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Re: Each of two carpenters, A and B, is working to build bookshelves. A, [#permalink]

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New post 17 Mar 2017, 13:06
1/6 + 1/10
5/30 + 3/30
8/30
30/8
15/4 which is answer A
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Re: Each of two carpenters, A and B, is working to build bookshelves. A, [#permalink]

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New post 18 Mar 2017, 08:31
Bunuel wrote:
Each of two carpenters, A and B, is working to build bookshelves. A, working alone, can complete the job in 10 hours. If B, working alone, can complete the job in 6 hours, how long will it take A and B working together to complete the job?

A. 15/4 hours
B. 15/2 hours
C. 8 hours
D. 39/4 hours
E. 16 hours



Time (working together) = AB/(A+B)= 60/16=15/4

Answer: A
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Re: Each of two carpenters, A and B, is working to build bookshelves. A, [#permalink]

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New post 19 Mar 2017, 05:39
Rate of A-1/10
Rate of B-1/6.

Rate when both A and B work together- 1/A + 1/B= 1/10 + 1/6= 16/60

So time taken by both = 60/16=15/4.

Hence answer is A.
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Re: Each of two carpenters, A and B, is working to build bookshelves. A, [#permalink]

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New post 20 Mar 2017, 04:02
Bunuel wrote:
Each of two carpenters, A and B, is working to build bookshelves. A, working alone, can complete the job in 10 hours. If B, working alone, can complete the job in 6 hours, how long will it take A and B working together to complete the job?

A. 15/4 hours
B. 15/2 hours
C. 8 hours
D. 39/4 hours
E. 16 hours



let the job be 60 units
rate of A = 60/10 = 6 units/hr
rate of B = 60/6 = 10 units/hr
working together, they will work with 10+6 = 16 units/hr

time taken to complete 60 units = 60/16 = 15/4 hrs
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Re: Each of two carpenters, A and B, is working to build bookshelves. A, [#permalink]

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New post 22 Mar 2017, 09:46
1
Bunuel wrote:
Each of two carpenters, A and B, is working to build bookshelves. A, working alone, can complete the job in 10 hours. If B, working alone, can complete the job in 6 hours, how long will it take A and B working together to complete the job?

A. 15/4 hours
B. 15/2 hours
C. 8 hours
D. 39/4 hours
E. 16 hours


We are given that the rate of carpenter A is 1/10 and the rate of carpenter B is 1/6. Thus, the combined rate is:

1/10 + 1/6 = 3/30 + 5/30 = 8/30 = 4/15. We use the work formula: work = rate x time, or work/rate = time. In this problem, the work is equal to one complete job, so work = 1 and rate = 4/15. Thus, it takes the two workers 1/(4/15) = 15/4 hours to complete the job.

Answer: A
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Re: Each of two carpenters, A and B, is working to build bookshelves. A,   [#permalink] 22 Mar 2017, 09:46
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