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Work/Rate

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Intern
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Joined: 16 Aug 2011
Posts: 11
Concentration: Finance, Entrepreneurship
GPA: 3.51
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Kudos [?]: 26 [0], given: 3

Work/Rate [#permalink] New post 15 Nov 2011, 23:53
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

80% (03:31) correct 20% (00:00) wrong based on 5 sessions
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose
A. 25 days
B. 30 days
C. 60 days
D. 65 days
E. 36 days

What's the best way to approach this?
[Reveal] Spoiler: OA

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Posts: 129
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Kudos [?]: 172 [2] , given: 6

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Re: Work/Rate [#permalink] New post 16 Nov 2011, 01:36
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Let A represent the number of days it would take Jose to complete the task if he worked alone (i.e. 1/A is Jose's work rate).
Let B represent the number of days it would take Jane to complete the task if he worked alone (i.e. 1/B is Jane's work rate).

Working together, Jose and Jane can complete an assigned task in 20 days.
20 (1/A + 1/B) = 1 (1)

However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days.

A/2 + B/2 = 45
A + B = 90
B = 90 - A (2)

Sub in (2) into (1):

20 (\frac{1}{A} + \frac{1}{{90-A}}) = 1

\frac{{(90-A)+A}}{{A(90-A)}} = \frac{1}{20}

\frac{{90}}{{90A-A^2}} = \frac{1}{20}

90A - A^2 = 1800

A^2 - 90A + 1800 = 0

(A - 60)(A - 30) = 0

So Jose's completion time on his own can be either 30 or 60 days. However, since the problem states that he is more inefficient than Jane, we can eliminate 30. Therefore, the answer is C: 60.
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Joined: 09 Sep 2011
Posts: 137
Location: United States (DC)
Concentration: General Management, Entrepreneurship
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Re: Work/Rate [#permalink] New post 16 Nov 2011, 01:41
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Hi

As you've got numbers in the answer choices, I'd prefer using the answer choices and working backwards to arrive at the required answer. It's always good to start with the middle/third option.
Also, if you can see numbers that might be related in some way (multiples, divisors, etc), try to use them.

In the question stem, we've got the numbers 20 and 45 - both are multiples of 5. So, I'd personally use a multiple of 5 present in the answer choices to begin with. Here, 4 of the 5 choices are multiples of 5, making it a bit difficult to choose a number - so I'd go with option 3.

Let the days taken by Jose be 'A' days and that taken by Jane be 'B' days. We're told that Jane is more efficient than Jose which means that Jane will take fewer number of days to complete the work as compared to Jose. Therefore, A > B

Now, using option C i.e. 60 days to be the time taken by Jose to complete the work,

Working together, A and B take 20 days to complete the work.
Therefore, 1/A + 1/B = 1/20
Substituting A = 60 and solving for B, we get B = 30 days

We know that Jose works and completes half of the work. Since Jose takes 60 days to complete the work, he would take 30 days to complete half the work.
Similarly, since Jane takes 30 days to complete the work, she would take 15 days to complete half the work.
So, in total, Jose and Jane take 45 days to complete the work - which is what is given in the question stem.

Hence Option C is the correct answer.

Hope this helps :)

Cheers!
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MBA Candidate 2015 | Georgetown University
McDonough School of Business

Re: Work/Rate   [#permalink] 16 Nov 2011, 01:41
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