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Abel can complete a work in 10 days, Ben in 12 days and Carl

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Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 03 Nov 2009, 11:21
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Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10
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Re: Word problem-work rate [#permalink] New post 03 Nov 2009, 11:27
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jade3 wrote:
Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10


B. 7

1/10 + 1/12 + 15 = 15/60 of the work done each day.

60 - 15/60-15/60 = 30/60 (abel then leaves)

Ben and carla working together finish 9/60 each day. Carla alone finished 4/60 each day so I figured the amount carla finishes alone will be a multiple of 4

30/60 - 9/60 = 21/60 (3 days total)
21/60-9/60 = 12/60 (4 days total; and coincidentally a multiple of 4) so assume carla works alone after this
12/60-4/60 = 8/60 (5 days)
8/60 - 4/60 = 4/60 (6 days)
4/60-4/60 = 0 (7 days)
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Re: Word problem-work rate [#permalink] New post 03 Nov 2009, 21:27
(1/A + 1/B + 1/C)*2 + (1/B + 1/C) ( N-2-3 ) + (1/C)*3 = 1

Solve for N, we get N = 7
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Re: Word problem-work rate [#permalink] New post 17 Oct 2013, 22:21
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Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 19 Oct 2013, 08:35
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asterixmatrix wrote:
Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10


Not to sound like a broken record from some of my earlier posts, but, worst case, you could always plug in answer choices for this problem.

Start with C and you get 2/10 of a job from Abel (which, notice, will always be the case), (8-3)/12 from Ben, and 8/15 from Carla.

LCM and add these up, and you get 12/60+25/60+32/60. Too much!

Do the same with B. Abel stays at 2/10, Ben is now 4/12, and Carla is 7/15. So, 12/60+20/60+28/60 = 60/60.

This approach could take longer in some circumstances, but it's always a default strategy where you have answer choices like these and no idea how to proceed.
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Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 03 Nov 2013, 11:37
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asterixmatrix wrote:
Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10


Responding to a pm.

First 2 days all three of them worked together, thus they did 2*(1/10 + 1/12 + 1/15) = 1/2 of the work.

Last 3 days only Carla worked, thus she did 3/15 = 1/5 of the work.

1 - 1/2 - 1/5 = 3/10 of the work was done by Ben and Carla: (time)*(combined rate)=(job done) --> t*(1/12 + 1/15) = 3/10 --> t = 2 days. So, we have that Ben and Carla worked together for 2 days.

Total days = 2 + 3 + 2 = 7.

Answer: B.

Hope it's clear.
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Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 18 Mar 2014, 06:30
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Let the work be completed in 't'.

Then again "Rate * Time = Work"

Rate(A)) = 1/10
Rate(B)=1/12
Rate(C)=1/15

Since A worked for 2 Days Work done by A= 2/10
Since B worked for 3 Days before work was completed work done B= (t-3)/12
Since C worked for full number of days = t/15

Adding them gives total work which is 1 unit.

2/10 + (t-3)/12 + t/15 = 1

Hence t=7
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Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 08 May 2014, 13:49
asterixmatrix wrote:
Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6
B. 7
C. 8
D. 9
E. 10


Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 3 days before the completion, this means that Carla had to work alone for these 3 days in which she completed 1/5 of the job.

Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 3/5

3/20 (t) = 3/5 ---> t = 4

Therefore, these 4 days worked plus the 3 days that Carla had to work by herself add to 7 days

Answer: B
Re: Abel can complete a work in 10 days, Ben in 12 days and Carl   [#permalink] 08 May 2014, 13:49
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