Dave can paint the office by himself in 4 hours. working with an associate, he can paint the
office in 3 hours. how long would it take his associate to do it working alone?

It would take 12 hours for his associate to do the complete work alone.

Step-by-step explanation:

Let 'x' be the hours taken by his associate working alone.

Given:

Time to paint the office by Dave is 4 hours.

Time to paint the office together is 3 hours.

Therefore, the part of work completed by Dave alone in 1 hour is

Part of work completed by an associate in 1 hour is

Now part of work completed by both in 1 hour is

Therefore,

Therefore, it would take 12 hours for his associate to do the complete work alone.