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# It would take one machine 4 hours to complete a large produc

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It would take one machine 4 hours to complete a large produc [#permalink]  17 Dec 2012, 05:29
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It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

(A) 7/12
(B) 1 1/2
(C) 1 5/7
(D) 3 1/2
(E) 7
[Reveal] Spoiler: OA
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Re: It would take one machine 4 hours to complete a large produc [#permalink]  17 Dec 2012, 05:33
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It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

(A) 7/12
(B) 1 1/2
(C) 1 5/7
(D) 3 1/2
(E) 7

The rate of the first machine is 1/4 job per hour;
The rate of the second machine is 1/3 job per hour;

Thus, the combined rate of the machines is 1/4+1/3=7/12 job per hour, which means that it takes 1/(7/12)=12/7 hours both machines to do the job.

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Re: It would take one machine 4 hours to complete a large produc [#permalink]  18 Jun 2013, 12:24
Bunuel wrote:
It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

(A) 7/12
(B) 1 1/2
(C) 1 5/7
(D) 3 1/2
(E) 7

The rate of the first machine is 1/4 job per hour;
The rate of the second machine is 1/3 job per hour;

Thus, the combined rate of the machines is 1/4+1/3=7/12 job per hour, which means that it takes 1/(7/12)=12/7 hours both machines to do the job.

Suppose we change the wording of the problem to "It would take 2 machines 4 hours together to complete a large production" How would you solve for that ? I'm trying to better understand the nature of the problem. Thanks. My logic says the rate is still the same since it still is 4 hours. If so than what does it change?
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Re: It would take one machine 4 hours to complete a large produc [#permalink]  06 Aug 2013, 21:49
how can the answer be C
in options dere is no option of 12/7
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Re: It would take one machine 4 hours to complete a large produc [#permalink]  06 Aug 2013, 21:54
arpana10july wrote:
how can the answer be C
in options dere is no option of 12/7

there is a typo in choice.

machine A takes 4 hr
machine B takes 3 hr
then together they will take = product /sum =$$(4*3)/(4+3)$$
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Re: It would take one machine 4 hours to complete a large produc [#permalink]  13 Oct 2013, 20:49
arpana10july wrote:
how can the answer be C
in options dere is no option of 12/7

12/7 is equivalent to 1 and 5/7
Re: It would take one machine 4 hours to complete a large produc   [#permalink] 13 Oct 2013, 20:49
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