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.