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Al can complete a particular job in 8 hours. Boris can

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Al can complete a particular job in 8 hours. Boris can [#permalink] New post 11 Jul 2006, 20:20
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Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours, how long, in hours, would it take Al, working alone, to finish the job?

A. 0.8
B. 3.0
C. 6.8
D. 8.0
E. 8.8
[Reveal] Spoiler: OA

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Re: PS: Work Problem [#permalink] New post 11 Jul 2006, 20:43
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X & Y wrote:
Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours, how long, in hours, would it take Al, working alone, to finish the job?

a. 0.8
b. 3.0
c. 6.8
d. 8.0
e. 8.8

all three people working together on the larger job for 2 hours=(1/16+1/10+1/8)*2=23/40
remaining part of the job is 17/40 Al's working rate is 1/16 hence
(17/40)/(1/16)=34/5 or 6.8 C it is
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Re: Work and time [#permalink] New post 03 Dec 2009, 22:49
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ro86 wrote:
Al can complete a particular job in 8 hours. Boris can complete the same job in 5. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours. How long, in hours, would it take Al, working alone to finish the job?

1. 0.8
2. 3.0
3. 6.8
4. 8.0
5. 8.8
I am confused as to how to evaluate the 2nd statement "Cody can complete a second job, which requires twice as much work as the first, in 8 hours"
Please explain!


the statement means if A and B are doing work "W" then Cody does a work which is "2W"
Now considering they work at the same workrate A will take 16hrs and B will take 10hrs to do the second job.
In 2hrs A,B and C will complete 2/16 + 2/10 + 2/8 = 92/160 part of the work
remaining work is 1-92/160 = 68/160
A does 1/16 part of second job in 1hr so he would require (68/160)/(1/16) = 6.8hrs
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 19 Mar 2012, 19:28
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Al's rate for smaller job = 1/8
Bigger job = 1/16

Boris rate for smaller job = 1/5
bigger job = 1/10

Cody's rate = 1/8


Work together for 2 hours on larger job

rate * time = work

(1/16+1/10+1/8) * 2 = work

work = 23/40

17/40 of the works remains

If Al was to work by himself to complete this then again

rate * time = work

1/16*time = 17/40

time = 6.8
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 05 May 2012, 06:38
I am stumped by this question.

Al's rate is 1 Job / 8 Hours
Boris's rate is 1 Job/ 5 Hours
Cody's rate is 2 Job /8 Hours

When the question states that the second job required "twice the amount of work as the first" how does one interpret this? In the above posts you have the the time doubled, ie, Al's rate is no longer 1/8 but 1/16 (so the time to complete the job was doubled). But I saw it more as his rate to complete the job stayed the same and the job grew by a multiple of 2, ie, (1/8)*time_Al=2 job
The rate should be doubled in the numerator and the denominator.So Al's rate of 1 Job/8 Hour becomes (2*1 Job/2*8 Hour)=2 Job/16 Hour
Very confused.
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 06 May 2012, 02:16
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alphabeta1234 wrote:
I am stumped by this question.

Al's rate is 1 Job / 8 Hours
Boris's rate is 1 Job/ 5 Hours
Cody's rate is 2 Job /8 Hours

When the question states that the second job required "twice the amount of work as the first" how does one interpret this? In the above posts you have the the time doubled, ie, Al's rate is no longer 1/8 but 1/16 (so the time to complete the job was doubled). But I saw it more as his rate to complete the job stayed the same and the job grew by a multiple of 2, ie, (1/8)*time_Al=2 job
The rate should be doubled in the numerator and the denominator.So Al's rate of 1 Job/8 Hour becomes (2*1 Job/2*8 Hour)=2 Job/16 Hour
Very confused.


Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours, how long, in hours, would it take Al, working alone, to finish the job?
A. 0.8
B. 3.0
C. 6.8
D. 8.0
E. 8.8

Al can complete a particular job in 8 hours, hence he can complete the second job which requires twice as much work as the first in 16 hours --> the rate of Al for this larger job is 1/16 job/hour;

Boris can complete a particular job in 5 hours, hence he can complete the second job which requires twice as much work as the first in 10 hours --> the rate of Boris for this larger job is 1/10 job/hour;

The rate of Cody for this larger job is 1/8 job/hour.

In 2 hours all three would complete 2*(1/16+1/10+1/8)=23/40 part of the larger job, so 17/40 part of it is left to be done.

Al can complete it in time=job/rate=(17/40)/(1/16)=34/5=6.8 hours.

Answer: C.

Hope it's clear.
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 07 May 2012, 17:39
Bunuel wrote:
alphabeta1234 wrote:
I am stumped by this question.

Al's rate is 1 Job / 8 Hours
Boris's rate is 1 Job/ 5 Hours
Cody's rate is 2 Job /8 Hours

When the question states that the second job required "twice the amount of work as the first" how does one interpret this? In the above posts you have the the time doubled, ie, Al's rate is no longer 1/8 but 1/16 (so the time to complete the job was doubled). But I saw it more as his rate to complete the job stayed the same and the job grew by a multiple of 2, ie, (1/8)*time_Al=2 job
The rate should be doubled in the numerator and the denominator.So Al's rate of 1 Job/8 Hour becomes (2*1 Job/2*8 Hour)=2 Job/16 Hour
Very confused.


Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours, how long, in hours, would it take Al, working alone, to finish the job?
A. 0.8
B. 3.0
C. 6.8
D. 8.0
E. 8.8

Al can complete a particular job in 8 hours, hence he can complete the second job which requires twice as much work as the first in 16 hours --> the rate of Al for this larger job is 1/16 job/hour;

Boris can complete a particular job in 5 hours, hence he can complete the second job which requires twice as much work as the first in 10 hours --> the rate of Boris for this larger job is 1/10 job/hour;

The rate of Cody for this larger job is 1/8 job/hour.

In 2 hours all three would complete 2*(1/16+1/10+1/8)=23/40 part of the larger job, so 17/40 part of it is left to be done.

Al can complete it in time=job/rate=(17/40)/(1/16)=34/5=6.8 hours.

Answer: C.

Hope it's clear.



I understand the solution, but i have to question the structure of the sentence "which requires twice as much work as the first". it is assumed that Al and Boris too takes twice the amount of time and that double time is not applicable solely to Cody.
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 08 May 2012, 00:09
Expert's post
jayaddula wrote:
Bunuel wrote:
alphabeta1234 wrote:
I am stumped by this question.

Al's rate is 1 Job / 8 Hours
Boris's rate is 1 Job/ 5 Hours
Cody's rate is 2 Job /8 Hours

When the question states that the second job required "twice the amount of work as the first" how does one interpret this? In the above posts you have the the time doubled, ie, Al's rate is no longer 1/8 but 1/16 (so the time to complete the job was doubled). But I saw it more as his rate to complete the job stayed the same and the job grew by a multiple of 2, ie, (1/8)*time_Al=2 job
The rate should be doubled in the numerator and the denominator.So Al's rate of 1 Job/8 Hour becomes (2*1 Job/2*8 Hour)=2 Job/16 Hour
Very confused.


Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours, how long, in hours, would it take Al, working alone, to finish the job?
A. 0.8
B. 3.0
C. 6.8
D. 8.0
E. 8.8

Al can complete a particular job in 8 hours, hence he can complete the second job which requires twice as much work as the first in 16 hours --> the rate of Al for this larger job is 1/16 job/hour;

Boris can complete a particular job in 5 hours, hence he can complete the second job which requires twice as much work as the first in 10 hours --> the rate of Boris for this larger job is 1/10 job/hour;

The rate of Cody for this larger job is 1/8 job/hour.

In 2 hours all three would complete 2*(1/16+1/10+1/8)=23/40 part of the larger job, so 17/40 part of it is left to be done.

Al can complete it in time=job/rate=(17/40)/(1/16)=34/5=6.8 hours.

Answer: C.

Hope it's clear.



I understand the solution, but i have to question the structure of the sentence "which requires twice as much work as the first". it is assumed that Al and Boris too takes twice the amount of time and that double time is not applicable solely to Cody.


Yes. We are told that "a second job, ... requires twice as much work as the first", so it's not only for Coby but for everyone.
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 10 May 2012, 05:05
I did another way, may be it is helpful.

Assume the work is W

as per the conditions: rate of Al: W/8; rate of Boris w/5 and rate of Cody 2w/8

they work together for 2 hours: 2w/8 + 2w/5 + 4w/8 = 46w/40; remaining work from the larger = 2w-46w/40 = 34w/40

thus. time * w/8 = 34w/40 ... time = 6.8
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 21 Sep 2012, 05:06
Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours, how long, in hours, would it take Al, working alone, to finish the job?

Bunuel ,question stem does not mention to find time for Al to complete remaining job.
I misunderstood the question and calculated time for Al to finish the whole job.
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 21 Sep 2012, 05:22
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bhavinshah5685 wrote:
Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job for 2 hours, how long, in hours, would it take Al, working alone, to finish the job?

Bunuel ,question stem does not mention to find time for Al to complete remaining job.
I misunderstood the question and calculated time for Al to finish the whole job.


I understand your point and agree that wording could have been better. Though notice that we are asked "how long, in hours, would it take Al, working alone, to finish the job?"
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 29 Mar 2014, 15:04
Answer C:

A rate = 1/8 (smaller job) or 1/16 (longer job)

B rate = 1/5 (smaller job) or 1/10 (longer job)

C rate = 1/4 (smaller job) or 1/8 (longer job)

((1/16)+(1/10)+(1/8))*2(hours) = 23/40 (work done in 2 hours) so rests for A, 17/40 to finish or 34/80.

A has a rate of 1/16 or 5/80. 34/5 = 6,8

Answer C
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Re: Al can complete a particular job in 8 hours. Boris can [#permalink] New post 30 Oct 2014, 00:16
Al's rate for large Job \(= \frac{1}{8} *\frac{1}{2} = \frac{1}{16}\)

Boris rate for Large Job \(= \frac{1}{5} * \frac{1}{2} = \frac{1}{10}\)

Cody's rate for large Job \(= \frac{1}{8}\)

Combined rate for Large Job\(= \frac{1}{8} + \frac{1}{10} + \frac{1}{16} = \frac{23}{80}\)

Work done (combined) in 2 hrs\(= \frac{23}{40} * 2 = \frac{23}{40}\)

Remaining work \(= 1- \frac{23}{40} = \frac{17}{40}\)

Time * Al's rate\(= \frac{17}{40}\)

Time required by Al\(= \frac{17}{40} * 16 = 6.8\)

Answer = C

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Re: Al can complete a particular job in 8 hours. Boris can   [#permalink] 30 Oct 2014, 00:16
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