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# work rate ps--plz solve

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work rate ps--plz solve [#permalink]  15 Feb 2010, 00:21
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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

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D
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Re: work rate ps--plz solve [#permalink]  15 Feb 2010, 06:03
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, 10:41, edited 1 time in total.
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Re: work rate ps--plz solve [#permalink]  15 Feb 2010, 08:42
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

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Re: work rate ps--plz solve [#permalink]  15 Feb 2010, 11:20
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

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]  15 Feb 2010, 16:41
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.
Re: work rate ps--plz solve   [#permalink] 15 Feb 2010, 16:41
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