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If it takes 6 identical printing presses exactly 4 hours to

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If it takes 6 identical printing presses exactly 4 hours to [#permalink]

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New post 10 May 2012, 04:14
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A
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C
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Question Stats:

78% (01:37) correct 22% (02:04) wrong based on 411 sessions

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If it takes 6 identical printing presses exactly 4 hours to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?

A. 3 hours, 20 minutes
B. 4 hours, 20 minutes
C. 4 hours, 48 minutes
D. 5 hours, 48 minutes
E. 6 hours, 50 minutes
[Reveal] Spoiler: OA
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Re: Work rate problem [#permalink]

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New post 10 May 2012, 04:22
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piyushksharma wrote:
If it takes 6 identical printing presses exactly 4 hours to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?

A. 3 hours, 20 minutes
B. 4 hours, 20 minutes
C. 4 hours, 48 minutes
D. 5 hours, 48 minutes
E. 6 hours, 50 minutes


6 presses - 5,000 newspapers - 4 hours ;
3 presses - 2,500 newspapers - 4 hours ;
3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000).

Answer: C.
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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]

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New post 28 Sep 2013, 02:08
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00:46 time taken to solve

Rate (6 machines) = 5000/4

Rate ( 1 machine) = 5000/24

Rate ( 3 machine ) = 5000/8

Rate * Time = Work

5000/8 * Time = 3000

Hence (C) !
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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]

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New post 28 Sep 2013, 02:28
piyushksharma wrote:
If it takes 6 identical printing presses exactly 4 hours to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?

A. 3 hours, 20 minutes
B. 4 hours, 20 minutes
C. 4 hours, 48 minutes
D. 5 hours, 48 minutes
E. 6 hours, 50 minutes


It is easier in this type of problems to find for unit measures and then find for the asked numbers.

1. 1 press would take 6*4 = 24 hours for 5000 newspapers
2. 1 press would take 24/5000 hrs for 1 newspaper
3. 3 presses would take 24/ (3* 5000) hrs for 1 newspaper
4. 3 presses would take 24*3000 / (3*5000) for 3000 newspapers i.e., 4.8 hrs which is 4 hours and 48 minutes.
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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]

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New post 01 May 2014, 20:51
I took the following approach..

Let e be the efficiency of each machine and t be the time that we need to find out.

So according to the question

6*e*4 = 5000 (given)

e = 5000/24 -- -- -- 1

Now you have the efficiency with you..

Simply solve for t..

3*e*t = 3000

t = 3000/(3*e)

From 1

t = 3000*24/3*5000

t = 4.8 hours

4 hours + 0.8*60 minutes

4 hours 48 minutes.

Option C is right :)
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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]

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New post 01 May 2014, 23:49
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Alternative way: The PTW Formula

PT/W = PT/W

where:
P = printer
T = time
W = work (newspapers)

(6)(4)/5000 = 3T/3000

Then use rapid cancellations:

24/5000 = T/1000
24/5 = T
T = 4 4/5 hrs
= 4 hrs 48 mins

Hope it helps! :)


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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]

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New post 18 Mar 2016, 22:42
piyushksharma wrote:
If it takes 6 identical printing presses exactly 4 hours to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?

A. 3 hours, 20 minutes
B. 4 hours, 20 minutes
C. 4 hours, 48 minutes
D. 5 hours, 48 minutes
E. 6 hours, 50 minutes

In 1 hour 1 press prints 208 and 1/3 newspapers (given)
In 3 hours 3*208 and 1/3 = 625 newspapers
To print 3000 newspapers 3000/625 = 4 hours 48 min
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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]

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New post 05 Feb 2018, 11:11
Hi All,

Since we have 6 machines working 4 hours each, we have 24 machine-hours of work being done. Those 24 hours of machine-work will produce 5,000 newspapers, so we can calculate what 1 hour of machine-work will produce:

5,000/24 = 2,500/12 = 1250/6 = 625/3 newspapers per machine-hour of work

With 3 machines, we have (625/3)(3) = 625 newspapers produced per hour. We're asked how many hours is takes to produce 3,000 newspapers under these conditions...

3,000/625 = 600/125 = 120/25 = 24/5 hours = 4 4/5 hours = 4 hours 48 minutes

Final Answer:
[Reveal] Spoiler:
C


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Re: If it takes 6 identical printing presses exactly 4 hours to   [#permalink] 05 Feb 2018, 11:11
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