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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 30 Aug 2008, 02:22
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?


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Re: time and work [#permalink] New post 30 Aug 2008, 14:06
arjtryarjtry wrote:
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?


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D

tough question for setting up a formula, took me forever

I solved this by substitution in reverse

For printer A:
24min --> 80 pages
6min --> 20 pages

If A takes 24 minutes to print 80 page, then for printer B
16min --> 80 pages
8min --> 40 pages
6min --> 30 pages

30 + 20 = 50 pages in 6 minutes
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Re: time and work [#permalink] New post 30 Aug 2008, 16:58
Here's the explanation;

For 40 pages

t[a] - t[b] = 4 min --> t[b] = t[a] + 4 ----- (1)

For 50 pages A and B take 6 min --> For 40 pages A and B takes 6/50*40 = 24/5 minutes

Now the equation when both A and B work together to finish a task is : t[a]*t[b]/(t[a] + t[b]) ----- (2)

Putting t[b] = t[a] + 4 from (1) equation (2) becomes:

5t[a]^2 - 68t[a] + 96 = 0 --> (5t[a]-8)(t[a]-12) = 0

---> t[a] = 12 (I discarded t[a] = 8/5 looking at the answer but not sure why it has to be excluded)

So, for 40 pages A takes 12 minutes ---> for 80 pages it will take 24 minutes!
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Re: time and work [#permalink] New post 30 Aug 2008, 19:49
for the GMAT , i think back solving is best...
but if the desire to display one's equation forming prowess is high..,
then resort to the conventional method. :wink:
the ans is D..
Re: time and work   [#permalink] 30 Aug 2008, 19:49
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