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Work Problem, How long does it take for one worker do it by himself?

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Intern
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Work Problem, How long does it take for one worker do it by himself? [#permalink]

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New post 08 Jan 2018, 11:14
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Worker A takes 8 hours to do a Job, Worker B & C takes 6 hours do that same job and Worker A and C takes 4 Hours to do that same job.

How long does it take for Worker B to do it by himself?

Bit confused on this one for myself :(
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Re: Work Problem, How long does it take for one worker do it by himself? [#permalink]

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New post 08 Jan 2018, 16:32
A does 1/8 of the job per hour. A and c together to 1/4 of the job per hour.
C must also do 1/8 of the job per hour.
B and c do 1/6 of the job per hour and c does 1:8.
B must do the rest. 1/6-1/8=1/24.
B does 1/24 of the job per hour so it takes him 24 hours.
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Re: Work Problem, How long does it take for one worker do it by himself? [#permalink]

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New post 08 Jan 2018, 22:04
chaosfirestorm wrote:
Worker A takes 8 hours to do a Job, Worker B & C takes 6 hours do that same job and Worker A and C takes 4 Hours to do that same job.

How long does it take for Worker B to do it by himself?

Bit confused on this one for myself :(

--------------

Lets convert the problem statement into equations:
Worker A takes 8 hours to do a Job, => a= 8 (a is the time required for worker A to complete the job)
Worker B & C takes 6 hours do that same job
=> 1/b + 1/c = 6 --(1)
(where b & c are the hours required for worker b & C to complete the job if done individually)
and Worker A and C takes 4 Hours to do that same job
=> 1/a + 1/c = 1/4
since a=8
1/c = 1/8

Substituting the value of c in (1) - we get 1/b = 1/24
Thus, it takes 24 hours for Worker B to do it by himself
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Re: Work Problem, How long does it take for one worker do it by himself? [#permalink]

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New post 08 Jan 2018, 22:27
It takes worker A and C 4 hours to do the job, half the time it takes A. So A and C work at equal speed. Therefore we van say it takes B and A 6 hours. A completes 3/4 of the job in 6 hours, so B does 1/4 of the job in 6 hours. So it takes her 24 hours to do the job on her own.

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Re: Work Problem, How long does it take for one worker do it by himself? [#permalink]

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New post 09 Jan 2018, 08:54
A * 8 = LCM(8,6,4)

(B+C)*6 = LCM(8,6,4)

(A+C)*4 = LCM(8,6,4)

A = 3
B+C = 4
A + C = 6

solving , B=1

B*1 = 24

Hence 24 hours
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Re: Work Problem, How long does it take for one worker do it by himself? [#permalink]

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New post 13 Jan 2018, 08:56
chaosfirestorm wrote:
Worker A takes 8 hours to do a Job, Worker B & C takes 6 hours do that same job and Worker A and C takes 4 Hours to do that same job.

How long does it take for Worker B to do it by himself?

Bit confused on this one for myself :(


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Re: Work Problem, How long does it take for one worker do it by himself?   [#permalink] 13 Jan 2018, 08:56
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