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Math Expert V
Joined: 02 Sep 2009
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At the Scholarly Text Printing Company, each of n printing presses ca  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 59% (02:08) correct 41% (02:01) wrong based on 46 sessions

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At the Scholarly Text Printing Company, each of n printing presses can produce on the average t books every m minutes. If all presses work without interruption, how many hours will be required to produce a run of 10,000 books?

(A) 10,000*60mn/t
(B) 10,000*60tm/n
(C) 10,000mn/(60t)
(D) 10,000m/(60nt)
(E) 10,000/(60mnt)

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At the Scholarly Text Printing Company, each of n printing presses ca  [#permalink]

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Bunuel wrote:
At the Scholarly Text Printing Company, each of n printing presses can produce on the average t books every m minutes. If all presses work without interruption, how many hours will be required to produce a run of 10,000 books?

(A) 10,000*60mn/t
(B) 10,000*60tm/n
(C) 10,000mn/(60t)
(D) 10,000m/(60nt)
(E) 10,000/(60mnt)

Algebraic Method

Since 1 printing press produces t books in m minutes, 1 printing press produces $$\frac{t}{m}$$ books in a minute.

In an hour, the printing press will produce $$\frac{60t}{m}$$ books. 'n' printing presses would produce $$\frac{60nt}{m}$$ books per hour.

Therefore, the presses need $$\frac{10000m}{60nt}$$ hours (Option D) to produce 10000 books.

Assuming numbers

1 printing press will produce (t = 10) books in (m = 6) minutes.
Therefore, 1 printing press produces $$\frac{5}{3}$$ books in a minute.
In an hour, the printing presses will produce $$60(\frac{5}{3}) = 100$$ books.
If there are (n=10) machines to do the work, every hour 1000 books are printed

In order to print 10000 books, it took the n printing presses $$\frac{10000}{1000} = 10$$ hours.

Substituting the values of t,m,and n in the answer options,

(A) 10,000*60mn/t = 10000*60*6*10/10 = 3600000 hours
(B) 10,000*60tm/n = 10000*60*10*6/10 = 3600000 hours
(C) 10,000mn/(60t) = 10000*10*10/60*6 = 100000/36 hours

(D) 10,000m/(60nt) = 10000*6/60*10*10 = 10 hours
(E) 10,000/(60mnt) = 10000/60*10*6*10 = 10000/36000 hours (Option D)
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Re: At the Scholarly Text Printing Company, each of n printing presses ca  [#permalink]

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Bunuel wrote:
At the Scholarly Text Printing Company, each of n printing presses can produce on the average t books every m minutes. If all presses work without interruption, how many hours will be required to produce a run of 10,000 books?

(A) 10,000*60mn/t
(B) 10,000*60tm/n
(C) 10,000mn/(60t)
(D) 10,000m/(60nt)
(E) 10,000/(60mnt)

It should be D
Each press produces $$t$$ books every $$m$$ minutes --> $$\frac{t}{m}$$ = $$\frac{t}{m}*60 \frac{minutes}{hour}$$ = $$\frac{60t}{m}$$ books per hour

$$n$$ presses would make $$\frac{n*60t}{m}$$ books per hour.

$$Rate * Time = Work$$
$$Time = Work/Rate$$
$$Time = \frac{10000}{60nt/m}$$
$$Time = 10000m/60nt$$
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Re: At the Scholarly Text Printing Company, each of n printing presses ca  [#permalink]

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_________________ Re: At the Scholarly Text Printing Company, each of n printing presses ca   [#permalink] 12 Apr 2019, 20:07
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