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

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

Wacks Formula - Math Shortcuts
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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]
piyushksharma
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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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

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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]
piyushksharma
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 machines --- 4 hours ----- 5000 prints

6 machines ----1 hour------5000/4 = 1250 prints

1 machine ------ 1 hour -----1250/6 prints

3 machine------1 hour------(1250/6)*3 = 1250/2 = 625 prints

Work = 3000 prints

Time required = 3000/625

4 hours 48 minutes

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

Take 6 Machines 4 hours for 5000
IN one hour 6 machines would produce 5000/4 = 1250
3 machine would produce half at constant rate i.e. 625
To produce 3000 newspapers then it would require 3000/625 = 4.8 or 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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Re: If it takes 6 identical printing presses exactly 4 hours to [#permalink]
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