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Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]
03 Nov 2009, 11:21

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Difficulty:

55% (hard)

Question Stats:

50% (04:06) correct
50% (02:44) wrong based on 208 sessions

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?

Re: Word problem-work rate [#permalink]
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)

Re: Word problem-work rate [#permalink]
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]
19 Oct 2013, 08:35

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Expert's post

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. _________________

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]
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.

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]
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 _________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]
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

gmatclubot

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