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A type A machine can complete a job in 5 hours and a type B

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A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 05:40
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (02:13) correct 27% (00:46) wrong based on 40 sessions
A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12
[Reveal] Spoiler: OA

Last edited by GMATT73 on 01 Dec 2005, 08:09, edited 1 time in total.
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 07:23
Can you, please elaborate on the meaning of" together and independently"
Thanx
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 07:40
BG wrote:
Can you, please elaborate on the meaning of" together and independently"
Thanx


I was also initially confused by such verbiage. However, this phrasing isn`t just Kaplish, it appears over and over again in various prep materials, so just accept it as "the machines/people/computers etc. work at their full capacity without complementing each other."

Hope that helps.
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:10
Matt I am getting 10/7

A need 5 hours to complete

and B needs 10 hours to compete

so 2A + 3B will complete 2/5 + 3/10 or 7/10 portion of the job in 1 hour

so the whole job will take 10/7 hours....

am I missing something.... :arh
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:12
remgeo wrote:
I am also getting 10/7

2*1/5 + 3*1/10 = 10/7


Even with the edit, you are still missing a step.
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:13
hik, it kept me pondering for a while ...wonder what i missed here (without the edition)
Matt, take good rest after such a busy week!!

Last edited by laxieqv on 01 Dec 2005, 08:16, edited 1 time in total.
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:16
now D should be the answer.


A need 5 hours to complete

and B needs 7 hours to compete

so 2A + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour

so the whole job will take 35/29 hours....
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:18
This is from the Kaplan White Course Book. The OE is a page long but makes no logical sense.
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:21
GMATT73 wrote:
remgeo wrote:
I am also getting 10/7

2*1/5 + 3*1/10 = 10/7


Even with the edit, you are still missing a step.


2*1/5 + 3*1/7 = 29/35

Ans = 35/29

I still cant see what step I missed :roll:
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:33
remgeo wrote:
GMATT73 wrote:
remgeo wrote:
I am also getting 10/7

2*1/5 + 3*1/10 = 10/7


Even with the edit, you are still missing a step.


2*1/5 + 3*1/7 = 29/35

Ans = 35/29

I still cant see what step I missed :roll:


The step highlighted in red. When did you decide to include it?
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 08:41
GMATT73 wrote:
remgeo wrote:
GMATT73 wrote:
remgeo wrote:
I am also getting 10/7

2*1/5 + 3*1/10 = 10/7


Even with the edit, you are still missing a step.


2*1/5 + 3*1/7 = 29/35

Ans = 35/29

I still cant see what step I missed :roll:


The step highlighted in red. When did you decide to include it?


Well, I had included that earlier as well.
10/7 was my conclusion
2/5 + 3/10 was the evidence
The assumption which is hidden was that I had taken the reverse of 7/10 to get the answer

:P :P
Dont you think I need some rest !!
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 01 Dec 2005, 09:22
Ans. D

My expl. A needs 5 hours to complete the job
2A need 5/2 hours to complete the job,


similarly 3B need 7/3 hours to complete the job


Lets consider 2A and 3B as single entity (X, Y)

so

1/X + 1/Y = 1/Z Z is the time to complete the job if working together.


1/(2/5) + 1/(7/3) =1/Z
2/5 + 3/7 =1/Z
29/35 = 1/Z

Z = 35/29

so if 2A and 3 B working together, they would need 35/29 hours to complete the job.


WORKING TOHETHER and INDEPENDENTLY means they work together without interfering each other hence they use their full potential to complete the job!

Does this sound sensible????


or simply.

1/5+1/5+1/7+1/7+1/7 =1/Z ( Z: time to work together)

Z = 35/29
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 02 Dec 2005, 13:01
Machine A's rate =1/5
Machine B's rate = 1/7

We have 2 A machines and 3 B machines = 1/5+1/5+1/7+1/7+1/7
Find the common denominator ie 35 and solve

You will get 29/35. This means that the machines can do 29/35 of the work in 1 hour. The question is asking how many hours does it take?

So, you take the inverse and you get 35/29.
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 02 Dec 2005, 15:48
Basic formula for the rate 1/a+1/b+1/c.....=1/Z time=Z

Rate for is A 1/5 and B works at the rate 1/7; 2A=2/5 and 3B=3/7

2/5+3/7=29/35 Flip it. 35/29. That Kaplish stuff can only appear at the beginning of Math section. Actual test questions appear to be much harder than that.
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Re: A type A machine can complete a job in 5 hours and a type B [#permalink] New post 26 Sep 2014, 11:50
A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

--just remember rate*time=job
Lets consider they both need to type for t hours to get the job done..

So, rate*time=job (Here job is 1 as it needs to be completed)
rate for type A machine =1/5 -- effective rate for 2 machines =2/5
similarly for type B machine effective rate for 2 machines =3/7

Finally we have,
(2/5)*t + (3/7)*t=1
t(29/35)=1
t=35/29

Answer D should be correct.
Re: A type A machine can complete a job in 5 hours and a type B   [#permalink] 26 Sep 2014, 11:50
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