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Work

by ketkoag » Fri Jun 19, 2009 5:07 pm
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and complete half the work 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 Jane is more efficient than Jose.
A. 25 days.
B.30 days.
C. 60 days.
D. 65 days
E. 36 days.

OA: C
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by cramya » Fri Jun 19, 2009 5:44 pm
let x and y be Jose and Jane's rate

Given xy/x+y = 20

xy = 20(x+y) (I)

x/2+y/2 = 45

x+y=90 (II)

xy = 1800

Solve for x using I and II
y=90-x

x(90-x) = 20(x+90-x)
x^2-90x+1800 = 0

(x cant be 30 since Jose is less efficient than Jane)


(OR)

plug in choices(I started with C since I saw 60 to be a factor of 1800 and then added 60+30 and got 20 days working together) and check x=60


C
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