Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/6 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?
Select:
A) 7
B) 9
C) 11
D) D.13
E) 18
rate of bob to paint n rooms is n/T(bob)   rate of Albert to paint n rooms is n/T(albert).   albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1   Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time   Therefore   n/x + n/x-1 = (3n/5)/(4/3) =   n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic   4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.   6*3 = 3n   18 = 3n.   Answer is 18
<result>E</result>
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/6 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?