Rate Problems

If each person paints at the same speed, then each one will paint one wall. It takes each person 32 minutes to paint one wall. So it takes 32 minutes for 12 people to paint 12 walls.

It takes 32 minutes for 8 people to paint 8 walls 

Then 8 people can paint 4 walls in (1/2)32 min  = 16 min

So...in 1 min...the 8 people can paint 1/4 of a wall

So......12 people will work 3/2 itmes as fast → painting 1/4 of a wall in 2/3 min

So...a whole wall will  take 12 people.....  4 * 2/3 min  = 8/3 min

And 12 walls will take  12 * 8/3 min  = 32 min

I believe it would take 32 minutes.

Via dimensional analysis:

8 people x 32 minutes   /  8 walls =  32   people - minutes / wall

12 walls / 12 people    x   32 people-minutes/wall =  32 minutes