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by niketdoshi123 » Thu Aug 09, 2012 4:19 am
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half of the work and then Jane takes over the task to complete the remaining half, 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) 23 days
b) 30 days
c) 36 days
d) 60 days
e) 65 days
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by Anurag@Gurome » Thu Aug 09, 2012 4:33 am
niketdoshi123 wrote:Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half of the work and then Jane takes over the task to complete the remaining half, 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) 23 days
b) 30 days
c) 36 days
d) 60 days
e) 65 days
Let us assume that Jose takes x days to complete the job and Jane takes y days to complete the same job.
Then 1 day work of Jose = 1/x
1 day work of Jane = 1/y
So, 1/x + 1/y = 1/20
(x + y)/xy = 1/20
20(x + y) - xy = 0 ... Equation (1)

Jose takes x/2 days to finish 1/2 the job.
Jane takes y/2 days to finish 1/2 the job.
Together, x/2 + y/2 = 45 implies x + y = 90 ... Equation (2)

From equations (1) and (2), (20 * 90) = x(90 - x)
1800 = 90x - x²
x² - 90x + 1800 = 0
(x - 60)(x - 30) = 0
x = 30, 60
But since Jane is more efficient, so x = 60.

The correct answer is D.
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by anuprajan5 » Thu Aug 09, 2012 4:42 am
The answer would be D.

Jose - x
Jane - y

1/x + 1/y = 1/20 - (1)

It also says x/2 + y/2 = 45 - (2)

Therefore x+y = 90 or x = 90-y

1/(90-y) + 1/y = 1/20

Solving y^2-90y+1800 = 0 which gives y = 30 or 60. Since Jane is more efficient, x can be 60 for Jose.
Last edited by anuprajan5 on Thu Aug 09, 2012 7:05 am, edited 1 time in total.
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by GMATGuruNY » Thu Aug 09, 2012 6:37 am
niketdoshi123 wrote:Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half of the work and then Jane takes over the task to complete the remaining half, 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) 23 days
b) 30 days
c) 36 days
d) 60 days
e) 65 days
We can plug in the answers, which represent the time for Jose to complete the job alone.
When Jose completes 1/2 the job and Jane completes 1/2 the job, t=45.
Since Jose is LESS efficient than Jane, his time alone must be GREATER than 45.
Eliminate A, B and C.

Let the job = 120 units.

Answer choice D: 60
Jose's rate = 120/60 = 2 units per day.
Combined rate for Jose and Jane = 120/20 = 6 units per day.
Thus, Jane's rate = combined rate - Jose's rate = 6-2 = 4 units per day.
Time for Jane to complete 1/2 the job = 60/4 = 15 days.
Time for Jose to complete 1/2 the job = 30 days.
Total time = 15+30 = 45 days.
Success!

The correct answer is D.
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