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

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

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24 May 2016, 22:19
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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
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Re: Five machines at a certain factory operate at the same constant rate  [#permalink]

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25 May 2016, 06:34
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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 do a work in 30 days..
1 machine will do that work in 30*4 days...
5 machines will do it in $$30*\frac{4}{5}= 24..$$
lesser time = $$30-24 = 6$$
C
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Re: Five machines at a certain factory operate at the same constant rate  [#permalink]

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25 May 2016, 00:19
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6
Total work done by 4 machines = 30 * 4 = 120 units

When one more machine is added each machine works for --> 120/5 = 24 hours

Difference = 30 - 24 = 6hrs

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Re: Five machines at a certain factory operate at the same constant rate  [#permalink]

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22 May 2018, 16:42
3
2
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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25 May 2016, 07:40
2
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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19 Oct 2018, 04:17
2
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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Five machines at a certain factory operate at the same constant rate  [#permalink]

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20 May 2018, 19:29
1
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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20 May 2018, 19:38
1
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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19 Aug 2018, 20:24
1
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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25 May 2016, 06:43
1
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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07 Jan 2017, 23:50
1
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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Re: Five machines at a certain factory operate at the same constant rate  [#permalink]

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20 Jun 2019, 03:33
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

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Re: Five machines at a certain factory operate at the same constant rate  [#permalink]

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04 Jan 2020, 05:29
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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Posts: 8
Re: Five machines at a certain factory operate at the same constant rate  [#permalink]

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06 Jan 2020, 09:13
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]

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06 Jan 2020, 21:49
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]

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22 Jan 2020, 05:07
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
Re: Five machines at a certain factory operate at the same constant rate   [#permalink] 22 Jan 2020, 05:07
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