Alright,

**Step 1**

Rate = how much work was done / total time

in other words

Rate = 1 wall / 12 days .... But this is the rate for THE WHOLE job

**Step 2**

We need to then determine how fast each painter works. meaning, the RATE of each painter.

Lets suppose the rate for 1 painter is X, so since we have 5 painters, we are going to have X+X+X+X+X = rate for THE WHOLE job

Lets simplify the above:

5X = 1/12...... solving for X and you have...

X = 1/60 <--this is the rate for 1 painter

**Step 3**

Now the easy part. The problem is giving us 6 painters, thats 6X = 6(1/60)

And the problem is also telling us that now, the wall is 50% bigger than the other wall.... so new wall = 1 + 1/2 = 1.5. The only thing we need to determine is how much time THE WHOLE JOB took to finish, lets call this value Y

Finally solve this:

6(1/60) = 1.5 / Y

and Y = 15 days

I hope this helped