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It takes printer A 4 more minutes than printer B to print 40

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It takes printer A 4 more minutes than printer B to print 40 [#permalink] New post 14 Feb 2010, 23:21
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Question Stats:

63% (03:35) correct 37% (02:54) wrong based on 47 sessions
It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

OPEN DISCUSSION OF THIS QUESTION IS HERE: it-takes-printer-a-4-more-minutes-than-printer-b-to-print-98479.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Sep 2013, 08:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: work rate ps--plz solve [#permalink] New post 15 Feb 2010, 05:03
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working together A and B can finish typing 40 pages = (6/ 50) * 40 = 24/5 mints.

Per unit work done by A and B is individually denoted by 1/A and 1/(A - 4) respectively.

Now Substituting all in the form of an equation,we have

1/A + 1/(A -4) = 5 / 24

We obtain a quadratic equation as ,

5A^2 - 68A + 96 = 0

Solving this equation A = 12 mints. Hence for 80 pages 12 * 2 = 24 mints.

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Last edited by amit2k9 on 15 Feb 2010, 09:41, edited 1 time in total.
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Re: work rate ps--plz solve [#permalink] New post 15 Feb 2010, 07:42
50 pages = 6 mins
40 pages = (6/50)*40 = \frac{24}{5}mins
40 pages = a + b (but a = b + 4mins)

Since each printer can do 1/a or 1/b work per unit, we can solve the equation:

1/a + 1/(a-4)= 5/24

Solved - like amit2k9 did - with a quadratic equation:

5a^2 - 68a + 96 = 0

a^2 - 68a/5 + 96/5 = 0

(a-8/5)*(a-60/5) = 0

a = 8/5 or a = 12 --> only 12 works

Hence, a needs 12 mins for 40 pages --> 24 mins = 80 pages

Answer "D"
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Re: work rate ps--plz solve [#permalink] New post 15 Feb 2010, 10:20
MSoS wrote:
50 pages = 6 mins
40 pages = (6/50)*40 = \frac{24}{5}mins
40 pages = a + b (but a = b + 4mins)

Since each printer can do 1/a or 1/b work per unit, we can solve the equation:

1/a + 1/(a-4)= 5/24

Solved - like amit2k9 did - with a quadratic equation:

5a^2 - 68a + 96 = 0

a^2 - 68a/5 + 96/5 = 0

(a-8/5)*(a-60/5) = 0

a = 8/5 or a = 12 --> only 12 works

Hence, a needs 12 mins for 40 pages --> 24 mins = 80 pages

Answer "D"


If you hate factoring, you could reason that the LCM of a and a - 4 is 24 and thus suspect that a is 12
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Re: work rate ps--plz solve [#permalink] New post 15 Feb 2010, 15:41
If you don't want to deal with quadratics this question is a good choice to just pick numbers.

\frac{1}{x} + \frac{1}{x+4} = \frac{5}{24}

\frac{1}{12} + \frac{1}{8} = \frac{5}{24}

x = 12, so the answer is 24.
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Re: work rate ps--plz solve [#permalink] New post 28 Sep 2013, 09:40
40/t + 40/(t+4) = 50/6

5t^2 -28t - 96 = 0

Substitute t=8 it satisfies

Hence time for 20 pages (t+4) =12
Time for 40 is 24

Hence (D) !
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Re: It takes printer A 4 more minutes than printer B to print 40 [#permalink] New post 29 Sep 2013, 08:26
Expert's post
Let the time needed to print 40 pages for printer A be a minutes, so for printer B it would be a-4 minutes.

The rate of A would be rate=\frac{job}{time}=\frac{40}{a} pages per minute and the rate of B rate=\frac{job}{time}=\frac{40}{a-4} pages per minute.

Their combined rate would be \frac{40}{a}+\frac{40}{a-4} pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is rate=\frac{job}{time}=\frac{50}{6}, so \frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}.

\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6} --> \frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}. At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find time needed for printer A to print 80 pages, then the answer would be 2a (as a is the time needed to print 40 pages). Answer D works: 2a=24 --> a=12 --> \frac{1}{12}+\frac{1}{8}=\frac{5}{24}.

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: it-takes-printer-a-4-more-minutes-than-printer-b-to-print-98479.html
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Re: It takes printer A 4 more minutes than printer B to print 40   [#permalink] 29 Sep 2013, 08:26
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