There are several ways to approach this question. This is my approach.
kathy takes 4 hours to paint 1 room
Rhonda takes 6 hours to paint 1 room
Kathy takes 24hrs to paint 6 room
Rhonda takes 24 hrs to paint 4 room
Together they can paint 10 rms in 24 hrs
Therefore 1 Room will take 24 / 10 = 2.4 hrs to painted by both of them
For the second question :
Let the number be x.
1/8x = 1/x + 1/(x-6)
Hope it helps.