If Amal, Kamal, and Ramal work together, it takes two hours to paint one room.
When Amal works alone, he can paint the same room in 6 hours. When Kamal
works alone, he can paint the same room in 4 hours. Determine how long it would
take Ramal to paint the room on his own.
Alan
Favorite Answer
A= amal's rate = (1/6) of the room per hour
K = Kamal's rate = (1/4) of the room per hour
R = Ramal's Rate
but for them together
(1/6)t + (1/4)t + Rt = 1 room
but when t = 2 , you get
(1/6)2 + (1/4)2 + 2R = 1
1/3 + 1/2 + 2R = 1
2/6 + (3/6) + 2R = 1
5/6 + 2R = 1
2R = 1 - 5/6 = 1/6
R = 1/6 / (2) = 1/12
Ramal paints 1/12 of a room per hour
so it takes him 12 hours to paint the room alone.
R's rate = 1/12
R Time = 12 hours
checking
(1/6)*2 + (1/4)*2 + (1/12)*2 =
4/12 + 6/12 + 2/12 = 1 room (it checks )