Working? alone, a person a can paint a room in 4 hr. person b can paint the same room working alone in 6 hr. how long will it take them if they work? together?

We will express the work done relative to time thus, 
person a = 1/4
person b = 1/6
Since two of them will work together and then add the two.
total work = person a + person b
                 = 1/4+1/6
                 =(3+2)/12
                 =5/12 hours
in hours
1/t=5/12 hours
total time = 2.4 hours or 2 hours and 24 mins.
The total time that person a and person b when working together will make the work done in 2.4 hours.