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M04-05

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M04-05  [#permalink]

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New post 15 Sep 2014, 23:22
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (01:12) correct 14% (01:39) wrong based on 162 sessions

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Robert can eat a 20 kg bag of potatoes in 10 days. If together with his wife, Jane, they can eat the same bag in 7 days, how many days does it take Jane to eat a 20 kg bag of potatoes by herself?

A. \(46\frac{2}{3}\)
B. \(23\frac{1}{3}\)
C. \(17\)
D. \(12\)
E. \(11\frac{2}{3}\)

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Re M04-05  [#permalink]

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New post 15 Sep 2014, 23:22
Official Solution:

Robert can eat a 20 kg bag of potatoes in 10 days. If together with his wife, Jane, they can eat the same bag in 7 days, how many days does it take Jane to eat a 20 kg bag of potatoes by herself?

A. \(46\frac{2}{3}\)
B. \(23\frac{1}{3}\)
C. \(17\)
D. \(12\)
E. \(11\frac{2}{3}\)


Build an equation as follows:

Let \(R\) denote Robert's and \(J\) denote Jane's "rate" of eating a 20 kg bag of potatoes.
\(R = \frac{1}{10}\)
\(J + R = \frac{1}{7}\)
\(J + \frac{1}{10} = \frac{1}{7}\)
\(J = \frac{1}{7} - \frac{1}{10} = \frac{10 - 7}{70} = \frac{3}{70}\)
\(\frac {1}{J} = \frac{70}{3} = 23\frac{1}{3}\)


Answer: B
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Re: M04-05  [#permalink]

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New post 26 Jun 2015, 06:46
Hello,

I am sorry but I am not getting the last step, could you, please, explain me :
If the result was 3/70
Why did you turn the fraction into 1/J=70/3

Thanks a lot,
Daniela
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Re: M04-05  [#permalink]

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New post 26 Jun 2015, 06:49
dmatinho wrote:
Hello,

I am sorry but I am not getting the last step, could you, please, explain me :
If the result was 3/70
Why did you turn the fraction into 1/J=70/3

Thanks a lot,
Daniela


J in the solution denotes the rate, we need time, which is reciprocal of rate, hence 1/J.

Hope it's clear.
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M04-05  [#permalink]

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New post 26 Jun 2015, 11:01
dmatinho wrote:
Hello,

I am sorry but I am not getting the last step, could you, please, explain me :
If the result was 3/70
Why did you turn the fraction into 1/J=70/3

Thanks a lot,
Daniela


The fraction 3/70 represents bags-of-potatoes/#days. To answer the question, you need the reciprocal, #days/bag-of-potatoes, which gives you the fraction 70/3. The question specifically asks how long does it take her to eat 1 bag of potatoes, so you need to divide the fraction through and get 23.3.
So it takes her 23.3(days)/1(bag-of-potatoes)
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Re: M04-05  [#permalink]

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New post 01 Jul 2015, 19:33
2
Every day Robert can eat 20/10 = 2Kg

Every day both can eat 20/7 Kg. So, everyday Jane can eat 20/7Kg - 2Kg = 6/7Kg

To eat 20Kg Jane needs 20/(6/7) = 70/3 days.
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Re: M04-05  [#permalink]

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New post 26 Dec 2016, 15:25
1
Robert Eats 14Kg in 7 days, so Jane will eat 6Kg in 7 days
6kg--->7Days
20kg--> x

x=20*7/6=70/3
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Re: M04-05  [#permalink]

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New post 08 Sep 2018, 18:58
Robert eats 20 kg in 10 days.

Robert and Jane together eat 20 kg in 7 days.

Jane eats 20 kg in how many days??

Since they eat 20 kg of potatoes, let's substitute the number of days into the Work Formula.

Using the work formula, let's denote "R" for Robert, "J" for Jane, and "T" for together

\(T = \frac{R * J}{R + J}\)

\(7 = \frac{10 * J}{10 + J}\)

70 + 7 J = 10 J

70 = 10 J - 7 J

70 = 3 J

\(\frac{70}{3} = J\)

\(J = 23 \frac{1}{3}\)


Answer B

Hope it helps!

Alecita :-)
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Re: M04-05 &nbs [#permalink] 08 Sep 2018, 18:58
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