Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second 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. Choose the correct choice from the following:
A) 25 days B) 30 days C) 60 days D) 65 days E) 36 days
Explanatory Answer   Step 1: Assign Variables and Frame Equations   Let Jose take 'x' days to complete the task if he worked alone.   Let Jane take 'y' days to complete the task if she worked alone.   Statement 1 of the question: They will complete the task in 20 days, if they worked together.   In 1 day, Jose will complete 1/x of the task.   In 1 day, Jane will complete 1/yof the task.   Together, in 1 day they will complete 1/20 of the task.   Therefore,1/x+ 1/y= 1/20.... (1)   Statement 2 of the question: If Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days.   Jose will complete half the task in x/2 days.   Jane will complete half the task in y/2 days.   ∴ x/2 + y/2= 45   Or, x + y = 90 or x = 90 - y .... (2)   Step 2: Solve the two equations and find x and y   Substitute the value of x as (90 - y) in the first equation   1/90−y + 1/y = 1/20   Or y2 - 90 + 1800 = 0.   The quadratic equation factorizes as (y - 60)(y - 30) = 0   So, y = 60 or y = 30.   If y = 60, then x = 90 - y = 90 - 60= 
<gadget id="calculator">90 - 60</gadget>
<output>30</output>
30 and   If y= 30, then x = 90 - y = 90 - 30= 
<gadget id="calculator">90 - 30</gadget>
<output>60</output>
60.   The question clearly states that Jane is more efficient than Jose. Therefore, Jane will take lesser time than Jose.   Hence, Jose will take 60 days to complete the task if he worked alone and Jane will take 30 days to complete the same task.   60 dayshoice 60 days
<result>C</result>
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second 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.