Problem:
Abe can paint the room in hours, Bea can paint percent faster than Abe, and Coe can paint twice as fast as Abe. Abe begins to paint the room and works alone for the first hour and a half. Then Bea joins Abe, and they work together until half the room is painted. Then Coe joins Abe and Bea, and they work together until the entire room is painted. Find the number of minutes after Abe begins for the three of them to finish painting the room.
Solution:
Abe paints at the rate of of the room per minute, Bea paints at the rate of of the room per minute, and Coe paints at the rate of of the room per minute. Thus together Abe and Bea paint at the rate of of the room per minute, and all three of them together paint at the rate of of the room per minute. Then in the first hour and a half Abe paints of the room. So together, Abe and Bea paint another of the room in minutes. Finally, Abe, Bea, and Coe paint together to paint half the room in minutes. The total time for painting the room is minutes.
The problems on this page are the property of the MAA's American Mathematics Competitions