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Work and Time - January 07, 2005
The GMAT Sample Math question for the day is from the topic Work and Time.
Question
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
The correct choice is (C) and the correct answer is 60 days.
Explanatory Answer
Let us assume that Jose will take x days to complete the task if he works alone and that Jane will take y days to complete the task if she worked alone.
From the information provided in the first statement of the question, we know that they will complete the task in 20 days, if they worked together on the task.
Therefore,
From the second statement, we can conclude that 
Or, x + y = 90 => x = 90 - y.
Substituting the value of x as 90 - y in the first equation, we get 
Or y2 - 90 + 1800 = 0.
Factorizing and solving for y, we get y = 60 or y = 30.
If y = 60, then x = 90 - y = 90 - 60 = 30 and
If y = 30, then x = 90 - y = 90 - 30 = 60.
As the question clearly states that Jane is more efficient than Jose, the second answer is the only possible alternative.
Hence, Jose will take 60 days to complete the task if he worked alone and Jane will take only 30 days to complete the same task.
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