Al working alone

[Vemuri]

Al can complete a particular job in 8 hrs. Boris can complete the same job in 5hrs. Cody can complete a second job, which requires twice as much work as the first, in 8hrs. If all three people work together on the larger job for 2hrs, 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

[cramya]

I would go with C ) 6.8

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

[vittalgmat]

I would go with C ) 6.8

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

Hi Cramya,
I have a question on how u got Cody's rate. The Q says that Cody can complete the second job which takes twice as long as the first in 8hrs.

I think this stmt is very ambiguous. I can interpret it in the multiple ways.

1. Cody can complete the first job as well as the second job in 8hrs. And 2nd job takes twice as long. ie. 1st job takes 2.67 hrs and 2nd job takes 5.33 hrs

2. Cody can complete "another job" which takes twice as long as first in 8 hrs. This implies that Cody can complete the first job in 4 hrs.


Pls comment....

thanks
-V

[cramya]

1. Cody can complete the first job as well as the second job in 8hrs. And 2nd job takes twice as long. ie. 1st job takes 2.67 hrs and 2nd job takes 5.33 hrs

Vittal,
I see where u r coming from but I am not sure if "Cody can complete a second job, which requires twice as much work as the first, in 8hrs" can be interpretted as

first job + second job = 8 hours

Instead I would think it would be

first job(1/2 work-> 4 hours) + 2nd job(1 work->8 hours) = 12 hours


Regards,
CR

[lilu]

Al's rate=1/16, Boris' rate=1/10, Cody's rate=1/8
Combined rate=1/16+1/10+1/8=23/80
In 2hrs the complete=23/80*2=23/40 of a job
Remaining job=17/40
It will take Al (Time=Work/Rate)-->(17/40)/1/16=34/5 OR 6.8hrs to finish the second job

[Vemuri]

I think this stmt is very ambiguous. I can interpret it in the multiple ways.

1. Cody can complete the first job as well as the second job in 8hrs. And 2nd job takes twice as long. ie. 1st job takes 2.67 hrs and 2nd job takes 5.33 hrs

2. Cody can complete "another job" which takes twice as long as first in 8 hrs. This implies that Cody can complete the first job in 4 hrs.


Pls comment....

thanks
-V

Your second interpretation is correct. If you see the framing of the question "Cody can complete a second job, which requires twice as much work as the first, in 8hrs", its using relative pronoun 'which' to add on that the second job takes twice as much work as the first job takes. So yes, interms of the first job Cody is pretty efficient & can finish the first job in just 4hrs.