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

Question

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

A. 0.8
B. 3.0
C. 6.8
D. 8.0
E. 8.8

iwillcrackgmat · Accepted Answer

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

Bunuel · Answer

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.

Yurik79 · Answer

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

kp1811 · Answer

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

alphabeta1234 · Answer

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.

jayaddula · Answer

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.

Bunuel · Answer

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.

pavanpuneet · Answer

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

bhavinshah5685 · Answer

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

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.

Bunuel · Answer

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?"

mvmarcus7 · Answer

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

PareshGmat · Answer

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

Bunuel: Kindly update OA .......

mvictor · Answer

the wording of the question is terrible...

ShashankDave · Answer

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)..

law258 · Answer

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

C

GMATinsight · Answer

Answer: Option C Screenshot 2020-08-11 at 8.32.33 PM.png

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

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