There are two ways to approach the wall painting problem:
- Walls per hour
- Hours per wall
For walls per hour, we know that Joe finishes a wall in 3 hour, so in one hour, he'll finish 1/3 of a wall. George finishes a wall in 2 hours, so he'll finish 1/2 of a wall in one hour. Together, they will finish 1/3 + 1/2, or 5/6 of a wall in one hour. (1/2=3/6, 1/3=2/6; 3/6+2/6 = 5/6). You can convert this to hours per wall by inverting the fraction ... 5/6 walls/hour -> 6/5 hours/wall. 4 walls at a rate of 6/5 hours per wall is 24/5 hours, or 4 + 4/5 hours, and 1/5 of an hour is 12 minutes, so 4/5 of an hour is 48 minutes. Time for 4 walls = 4 hours + 48 minutes.
For hours per wall, the least common multiple for Joe and George's rates is 6 hours. In 6 hours, Joe finishes 2 walls, and George finishes 3 walls, so together they finish 5 walls in 6 hours. That is 6/5 hours per wall. And as we calculated before, 4 walls at 6/5 hours per wall is 4 hours and 48 minutes.