Working alone, John finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. John alone cleans the entire house in 6 hours. How many hours will it take Nick and John to clean the entire house if they work together?
Choose the correct answer:
A) 1.5  B) 2  C) 2.4  D) 3  E) 3.6

Rationale: answer is 3.6 hours . john does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
Answer: E