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Jane is more efficient than Jose

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Jane is more efficient than Jose

by sanju09 » Wed Feb 18, 2009 6:05 am
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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by bluementor » Wed Feb 18, 2009 7:44 am
Jane takes x days to complete the task alone.
Jose takes y days to complete the task alone.

Jane is more efficient than Jose, therefore, x<y.

1/x + 1/y = 1/20
xy/(x+y) = 20 ….eqn 1

x/2 + y/2 = 45
x + y = 90
x = 90 - y …… eqn 2

Solving equations 1 and 2:

(90 - y)y/(90-y + y) = 20
90y - y^2 = 1800
y^2 - 90y + 1800 = 0
(y - 60)(y - 30) = 0

Therefore, y = 30 or 60. Since y > x, therefore y = 60. Choose C.

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