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# How long would it take Joan to count the books in a small library?

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Math Expert
Joined: 02 Sep 2009
Posts: 58393
How long would it take Joan to count the books in a small library?  [#permalink]

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24 Jan 2016, 05:37
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Difficulty:

5% (low)

Question Stats:

91% (00:36) correct 9% (00:49) wrong based on 104 sessions

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How long would it take Joan to count the books in a small library?

(1) She counts twice as fast as Emily.
(2) Working together, Joan and Emily count the books in 26 hours.

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Joined: 03 Jan 2015
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Re: How long would it take Joan to count the books in a small library?  [#permalink]

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24 Jan 2016, 14:06

(1) She counts twice as fast as Emily.

J = 2E. Not sufficient
(2) Working together, Joan and Emily count the books in 26 hours.
J + E = 26. Not sufficient

Together, you can solve for J. Answer choice C.
SVP
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Re: How long would it take Joan to count the books in a small library?  [#permalink]

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25 Jan 2016, 01:38
Bunuel wrote:
How long would it take Joan to count the books in a small library?

(1) She counts twice as fast as Emily.
(2) Working together, Joan and Emily count the books in 26 hours.

combines Rate (R) = RJ + RE; RJ=Joan rate & RE=Emily rate

1) RJ=2RE ......Ins

2)Combines Rate= 1/26....ins

Combined 1& 2

RJ+RE=1/26....> 1/26= RJ+ 1/2 (RE)..............Suf

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Re: How long would it take Joan to count the books in a small library?  [#permalink]

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25 Jan 2016, 13:33
Bunuel wrote:
How long would it take Joan to count the books in a small library?

(1) She counts twice as fast as Emily.
(2) Working together, Joan and Emily count the books in 26 hours.

One C for me.
(1) We did not know how long Emily took to count the books in the lib --> insufficient.
(2) We did not know the rate between Emily and Joan in counting the books--> insufficient.
(1) & (2)--> support to each other
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Re: How long would it take Joan to count the books in a small library?  [#permalink]

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04 Feb 2016, 10:35
1
I am really bad at these sorts of problems so could someone check to see if this is correct?

Given that I understand that both statements together are sufficient, is the math correct?

1. She counts twice as fast as Emily.
Joans rate is $$\frac{1}{x}$$ and Emilys rate is $$\frac{1}{x}*\frac{1}{2}$$ because it is half of Joans

2.Working together, Joan and Emily count the books in 26 hours.

$$\frac{1}{26}=\frac{1}{x}+\frac{1}{2x}$$
$$\frac{1}{26}=\frac{3}{2x}$$
$$78=2x$$
$$x=39$$

Joans rate is $$\frac{1}{39}$$ and Emilys rate is $$\frac{1}{78}$$
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Re: How long would it take Joan to count the books in a small library?  [#permalink]

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17 Oct 2018, 10:25
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Re: How long would it take Joan to count the books in a small library?   [#permalink] 17 Oct 2018, 10:25
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