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It would take one machine 4 hours to complete a large production order

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It would take one machine 4 hours to complete a large production order [#permalink]

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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) \(\frac{7}{12}\)

(B) \(1 \frac{1}{2}\)

(C) \(1 \frac{5}{7}\)

(D) \(3 \frac{1}{2}\)

(E) 7
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Walkabout 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) \(\frac{7}{12}\)

(B) \(1 \frac{1}{2}\)

(C) \(1 \frac{5}{7}\)

(D) \(3 \frac{1}{2}\)

(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 \(\frac{1}{4}+\frac{1}{3}=\frac{7}{12}\) job per hour, which means that it takes \(\frac{1}{(\frac{7}{12})}=\frac{12}{7}=1 \frac{5}{7}\) hours both machines to do the job.

Answer: C.
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Re: It would take one machine 4 hours to complete a large production order [#permalink]

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New post 18 Jun 2013, 13:24
Bunuel wrote:
Walkabout 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.

Answer: C.


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 production order [#permalink]

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New post 06 Aug 2013, 22:49
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 production order [#permalink]

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New post 06 Aug 2013, 22:54
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 production order [#permalink]

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New post 13 Oct 2013, 21:49
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

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Re: It would take one machine 4 hours to complete a large production order [#permalink]

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Walkabout 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


We can classify this problem as a “combined worker” problem. To solve this type of problem we should use the formula:

Work (done by worker 1) + Work (done by worker 2) = Total Work Completed

It takes machine one 4 hours to complete a job, so the rate of machine one is ¼. It takes machine two 3 hours to complete a job, so the rate of machine two is 1/3. Since we know they are both working together to complete the job, we can label this unknown time as “t” for each machine during the time that both machines are working together. Since rate x time = work, we can multiply to get the work completed for each machine.

Image

Finally, we can plug our two work values into the combined work formula and determine t. Since the job is completed, the total work completed is 1.

Work (done by worker 1) + Work (done by worker 2) = Total Work Completed

(1/4)t + (1/3)t = 1

Multiplying the entire equation by 12 gives us:

3t + 4t = 12

7t = 12

t = 12/7 = 1 5/7

Answer is C.
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Re: It would take one machine 4 hours to complete a large production order [#permalink]

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Walkabout 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


Another approach is to assign the ENTIRE job a certain number of units.
The least common multiple of 4 and 3 is 12.
So, let's say the ENTIRE production order consists of 12 widgets.

It would take one machine 4 hours to complete a large production...
Rate = output/time
So, this machine's rate = 12/4 = 3 widgets per hour

...and another machine 3 hours to complete the same order.
Rate = units/time
So, this machine's rate = 12/3 = 4 widgets per hour

So, their COMBINED rate = 3 + 4 = 7 widgets per hour.

Working simultaneously at their respective constant rates, to complete the order?
Time = output/rate
= 12/7 hours

Answer:
[Reveal] Spoiler:
C


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It would take one machine 4 hours to complete a large production order [#permalink]

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New post 23 Sep 2017, 06:42
JeffTargetTestPrep Bunuel

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When we are given t as 3 and 4 hours why are we still assigning an unknown variable?
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It would take one machine 4 hours to complete a large production order   [#permalink] 23 Sep 2017, 06:42
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