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# Five machines at a certain factory operate at the same constant rate

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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

Total work = 4*30 machine hrs

Time taken = 4* 30 /5 => 24 hours...

Thus all five machines, operating simultaneously will take ( 30 - 24 ) 6 hours..

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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

If 4 machines take 30 hrs, 5 machines will take 30*4/5= 24 hrs

How many fewer hours will all five machines take= 30-24= 6 hrs

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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

Let the rate of machine be x hours. So in hour it can complete 1/x of work. Four machine rate = 4*(1/x) = 4/x.
Now, Rate* Time = Job i.e. 4/x*30 = Job. So one machine can take 120 hour to complete the job.
Five machine works together it can take :120/5 = 24 hours to complete the job.
Hence 30-24 = 6 hours.

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Five machines at a certain factory operate at the same constant rate [#permalink]
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Hi VeritasPrepKarishma chetan2u niks18 gmatbusters Bunuel

Let me know if my below approach is correct using 'Joint variation'
as discussed here

I have to find number of hrs when machines operating are increased from 4 to 5.
Simple logic says if I increase the no of machines, the no of hrs to complete the same work
will be reduced. Hence if I have initial no. of hrs defined, I need to multiply it by proper fraction
ie numerator/denominator < 1

Using above steps:

No of hrs = 30 (when 4 machines are operational)
I need to multiply this by 4/5 since I need a fraction less than 1.
Hence I get 30 * (4/5) = 24 as hrs required when 5 machines are operational.

I already know that when 4 machines are working, I shall need 30 hrs.
Hence, difference = 30-24 ie 6 hrs.
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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Hi VeritasPrepKarishma chetan2u niks18 gmatbusters Bunuel

Let me know if my below approach is correct using 'Joint variation'
as discussed here

I have to find number of hrs when machines operating are increased from 4 to 5.
Simple logic says if I increase the no of machines, the no of hrs to complete the same work
will be reduced. Hence if I have initial no. of hrs defined, I need to multiply it by proper fraction
ie numerator/denominator < 1

Using above steps:

No of hrs = 30 (when 4 machines are operational)
I need to multiply this by 4/5 since I need a fraction less than 1.
Hence I get 30 * (4/5) = 24 as hrs required when 5 machines are operational.

I already know that when 4 machines are working, I shall need 30 hrs.
Hence, difference = 30-24 ie 6 hrs.

Yes, absolutely correct.
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

The rate of 4 machines is 1/30.

We can let the rate of 5 machines be n and create the equation:

4/(1/30) = 5/n

120 = 5/n

120n = 5

n = 5/120 = 1/24

So it will take 1/(1/24) = 24 hours for the 5 machines to fill the same order and thus it takes 6 fewer hours than if the order were filled by 4 machines.

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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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Rate if 4 machines 1/30
Rate of 1 machine = 1/(30*4)
Rate of 5 machines = 1*5/(30*4) = 1/24
So 5 machines complete work in 24 hourse and take 6 fewer hours.

Posted from my mobile device
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

The question asks for the difference in hours

4 machines finish in 30 hours so 1 machine finishes in 120 hours.

5 machines will then finish in 120/5 = 24 hours.

The difference in hours is |24-30| = 6.

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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
Hi can someone tell me where did I go wrong.

If 4 machines require 30 hours? So 5 machines will be 30*5/4?

I don’t know where have I gone wrong

Posted from my mobile device
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

4 machines take -> 30 hours
1 machine takes -> 30*4 hours
5 machines take -> 30*4/5 hours
Difference = 30*4/5-30= 6 hours

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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
If 4 machines take 30 hrs, 5 machines will take 30*4/5= 24 hrs

#fewer hours= 30-24= 6 hrs
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
Shef08 wrote:
Hi can someone tell me where did I go wrong.

If 4 machines require 30 hours? So 5 machines will be 30*5/4?

I don’t know where have I gone wrong

Posted from my mobile device

Even though this is a late reply, you need to look at it this way.

4 machines require 30 hours so that would mean 1 machine require 120 hours. (4 * 30 = 120)

Now you need to find how many hours will it require 5 machines to do the same job. 120/5 = 24

In your calculation it should be (30 * 4)/5
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
4 machine 30 day -> 1 machine 120 day(cause it takes 4 times many for 1 machine to fill the order) -> 5 machine 24 day -> 30-24=6 day less
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Five machines at a certain factory operate at the same constant rate [#permalink]
nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

Here's my approach
I use proportionality.

W = Rate * Time
given Rate is constant, we have a direct relation of proportionality
W is directly proportional to Time

*I factor is Machines with Time, since I am only comfortable with 2 variable.
So.

W = R* 4Machines * 30 hrs )Or 120 [forget about the R, since its proportional dosent matter, R will get cancelled anyway]
W = R* 5Machines *?hrs) w = or 5? hrs.

This means for the same work, at the same rate, 5*? = 120
? = 24 = 24 hrs

30-24 = 6hrs less
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

chetan2u Bunuel
My question is nothing new but 'Old wine new bottle'. Can we say this?

Since all 5 machines work at a same constant rate, it can be said that either 5 do the work of 4 or 4 do the same work more(+25%) efficiently. If 4 machines do the work they perform the work with an individual efficiency that is 25% better than each machine's previous efficiency -

As the word 'simultaneously' is used each of the 4 machines do 30 hours work, totalling 120 hours of work. So, 120 hours of work when completed by 5 machines each work 24 hours. Thus, they each took 6 hours less or in other words they performed the work more efficiently - together efficiency improved by $$\frac{6}{30}*100 = 20%$$ for 5 machines. We can also say that individually each machine performed with 25% more(1 machine's work divided among 4 machines) efficiency. Thus, each take $$\frac{30}{1.25} = 24$$ hours. Answer is 30 - 24 = 6 hours.

OR

If we ignore(only when all the machines work at same constant rate) the the word 'simultaneously' and take machines to be working consecutively one after the other, each of the 4 machines take $$\frac{30}{4} = 7.5$$ hours. Now that 5 machines are going to do the same work, it can be said that 4 can do the same work if each of them work at 1.25times rate(since 1 machine's work is distributed among 4). So the 4 machines now take $$\frac{7.5}{1.25} = 6$$ hours and total time is 24 hours. Hence answer is 30 - 24 = 6 hours.

Second scenario is just to understand the question better. Can we say that?
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Re: Five machines at a certain factory operate at the same constant rate [#permalink]
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We have 5 machines in a certain factory:

Four of these machines take 30 hours to fill a production order.

Therefore one machine takes 120 hours to fill a production order.

How many fewer hours does it take 5 machines to fill this order?

120 hours split by 5 machines = 24 hours per machine.

30 - 24 = 6 fewer hours.

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Five machines at a certain factory operate at the same constant rate [#permalink]
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nalinnair wrote:
Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

Five matchines will take (4*30)/6 = 24 hours

30-24 = 6 fewer hours will require.
Ans. C
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