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# Working together, Jose and Jane can complete an assigned

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Joined: 11 Mar 2007
Posts: 154
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Working together, Jose and Jane can complete an assigned [#permalink]  19 Aug 2007, 21:15
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
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Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
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Jose -> 1 job in x days -> 1/x job in 1 day
Jane -> 1 job in y days -> 1/y job in 1 day

Together, 1/x + 1/y = 1/20
x+y/xy = 1/20
20x+20y = xy

Jose takes x/2 days to finish 1/2 a job. Jane takes y/2 days to finish 1/2 a job. Together, x/2 + y/2 = 45 --> x+y = 90

So

20(x+y) = xy
20(90) = x(90-x)
1800 = 90x - x^2
x^2 - 90x + 1800 = 0
x = 60 days or 30 days. But we are told Jane is more efficient, so x = 60 days.
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