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

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Director
Joined: 11 Jun 2007
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It takes printer A 4 more minutes than printer B to print 40 [#permalink]  31 Oct 2007, 22:44
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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Manager
Joined: 30 Oct 2007
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Re: rate [#permalink]  01 Nov 2007, 01:37
beckee529 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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Lets say printer B takes b minutes to print 40 pages then A will need (b+4) minutes to print 40 pages. Together they need 6 mniutes to print 50 pages.

40/b + 40/(b+4) = 50/6
24(2b+4) = 5(b pow 2+ 4b)

Solving quadratic equation gives b = 8 or -2.4, for sure - time is not feasible. Therefore A needs 8+4 = 12 minutes to print 40 pages hence 24 minutes to print 80 pages.

Director
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I had the same setup equation, but that quadratic equation is BRUTAL.
Director
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sonibubu wrote:
I had the same setup equation, but that quadratic equation is BRUTAL.

yup thats why i posted the question.. to see if anyone else had another approach to avoid quadratic eqn

so far nil..
Manager
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beckee529 wrote:
sonibubu wrote:
I had the same setup equation, but that quadratic equation is BRUTAL.

yup thats why i posted the question.. to see if anyone else had another approach to avoid quadratic eqn

so far nil..

Suppose A takes 20 minutes for 80 pages. Then A's rate is 4 pages per minute, or 40 pages in 10 minutes. B's rate is 40 pages in 6 minutes, or 40/6. Combined, their rates are 4 + (40/6) = 64/6, which is greater than 50/6. So the rate for A yielded by this answer choice is too high. A must take more than 20 minutes to print 80 pages.

So move on to D. A's rate is 80/24 or 10/3 pages per minute. A takes 12 minutes for 40 pages, so B takes 8, and B's rate is 40/8 = 5. Their combined rate is 10/3 + 5 = 10/3 + 15/3 = 25/3 = 50/6. There's the answer.
Manager
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johnrb wrote:
beckee529 wrote:
sonibubu wrote:
I had the same setup equation, but that quadratic equation is BRUTAL.

yup thats why i posted the question.. to see if anyone else had another approach to avoid quadratic eqn

so far nil..

Suppose A takes 20 minutes for 80 pages. Then A's rate is 4 pages per minute, or 40 pages in 10 minutes. B's rate is 40 pages in 6 minutes, or 40/6. Combined, their rates are 4 + (40/6) = 64/6, which is greater than 50/6. So the rate for A yielded by this answer choice is too high. A must take more than 20 minutes to print 80 pages.

So move on to D. A's rate is 80/24 or 10/3 pages per minute. A takes 12 minutes for 40 pages, so B takes 8, and B's rate is 40/8 = 5. Their combined rate is 10/3 + 5 = 10/3 + 15/3 = 25/3 = 50/6. There's the answer.

Nice approach, far better than solving equations
But i think time taken solving equations and going through answer choices is almost same even starting from A may take much more time.

** One has to be careful when comparing 25/3 to 50/6 because one is expecting an answer that matches with 50/6 while answer is 25/3 that can lead to a wrong decision taken quickly
CEO
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beckee529 wrote:
sonibubu wrote:
I had the same setup equation, but that quadratic equation is BRUTAL.

yup thats why i posted the question.. to see if anyone else had another approach to avoid quadratic eqn

so far nil..

Haha ya I got to 0=50t^2-480t-760 and then i was like ya right... comon lol
CEO
Joined: 21 Jan 2007
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johnrb wrote:
beckee529 wrote:
sonibubu wrote:
I had the same setup equation, but that quadratic equation is BRUTAL.

yup thats why i posted the question.. to see if anyone else had another approach to avoid quadratic eqn

so far nil..

Suppose A takes 20 minutes for 80 pages. Then A's rate is 4 pages per minute, or 40 pages in 10 minutes. B's rate is 40 pages in 6 minutes, or 40/6. Combined, their rates are 4 + (40/6) = 64/6, which is greater than 50/6. So the rate for A yielded by this answer choice is too high. A must take more than 20 minutes to print 80 pages.

So move on to D. A's rate is 80/24 or 10/3 pages per minute. A takes 12 minutes for 40 pages, so B takes 8, and B's rate is 40/8 = 5. Their combined rate is 10/3 + 5 = 10/3 + 15/3 = 25/3 = 50/6. There's the answer.

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