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Manager  Joined: 25 May 2006
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Al can complete a particular job in 8 hours. Boris can  [#permalink]

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3
17 00:00

Difficulty:   75% (hard)

Question Stats: 65% (02:48) correct 35% (03:01) wrong based on 518 sessions

### HideShow timer Statistics 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

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Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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5
2
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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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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1
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"

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]

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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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Joined: 02 Sep 2009
Posts: 56277
Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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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.

Hope it's clear.
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Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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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.

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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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.

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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Posts: 92
Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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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]

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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?

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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Joined: 02 Sep 2009
Posts: 56277
Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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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]

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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

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Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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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$$= \frac{17}{40} * 16 = 6.8$$

Bunuel: Kindly update OA .......
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Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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the wording of the question is terrible...
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Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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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

Let the total(original) job be 40 units..larger is 80 units

Al's units per hour = 40/8 = 5 units
Similarly
Boris' = 8 units
Cody's = 10 units

in 2 hrs they together complete 46 units
Units left for the larger job = 80 - 46 = 34 units

Al's time for the rest of this job = 34/5 = 6.8(C)..

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Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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Al --> 40 bricks = R x 8hrs --> R=5

Boris --> 40 bricks = R x 5hrs --> R=8

Cody --> 80 bricks = R x 8hrs --> R = 10

Al + Boris + Cody --> 2 hours spent together on larger job (aka 80 bricks)
20+10+16=46
80-46 = 34 bricks remain for Al to complete on his own

How long will it take Al?
W=RxT --> 34=5T --> 6.8 hrs

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Re: Al can complete a particular job in 8 hours. Boris can  [#permalink]

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_________________ Re: Al can complete a particular job in 8 hours. Boris can   [#permalink] 07 Mar 2018, 18:20
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