A professional janitor can clean a certain high school in (4+4) hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?	Choose the correct choice.
A) - $ 56	B) - $ 6	C) $ 0	D) $ 6	E) $ 8

Rationale: a professional janitor can clean a certain high school in ( 4 + 4 ) or 8 hours so ( applying rule # 1 ) , the janitor can clean 1 / 8 of the school in one hour a student sentenced to detention can clean that same high school in 20 hours so ( applying rule # 1 ) , the student can clean 1 / 20 of the school in one hour so , combined , the student and janitor can clean ( 1 / 8 + 1 / 20 ) of the school in one hour 1 / 8 + 1 / 20 = 5 / 40 + 2 / 40 = 7 / 40 so , in one hour they can clean 7 / 40 of the school . applying rule # 2 , it will takethem 40 / 7 hoursto clean the entire school . the janitor earns $ 21 / hour and the student earns $ 7 / hour , so their combined rate is $ 28 / hour . theircombined wages = ( pay rate ) ( time ) = ( $ 28 / hour ) ( 40 / 7 hours ) = $ 160 working alone , the janitor takes 8 hours and earns $ 21 / hour so , working alone , the janitor ' s earnings = ( pay rate ) ( time ) = ( $ 21 / hour ) ( 8 hours ) = $ 168 $ 168 - $ 160 = $ 8 , so the answer is e
Answer: E