Working together, Jose and Jane can complete an assigned task in 12 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 48 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 answers
A) 25 days	B) 30 days	C) 60 days	D) 65 days	E) 36 days

Rationale: assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 12 12 ( x + y ) = xy next , we ' re told 1 job takes 48 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 48 x + y = 96 so xy = 1152 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 36 days for jose and 32 days for jane . answer : e
Answer: E