I very much doubt there is any formula or rule of thumb for exactly this problem. It seems the question was merely brought up to see if you can apply the basic rules of thumb that do exist.
By approximation, your turn radius will be 1/200 of your ground speed. So, at 180 kt you'll need roughly 1.8 NM for the turn. I would round this up and continue with 2 NM. Using the 1:60 rule, you can estimate that, for a 30 degrees' base turn angle, you'll have these 2 miles once you're 4 miles out. Now, how long does it take to fly 4 miles at a speed of 180 knots? Answer: 1:20 minutes.
Sounds easy, doesn't it. But I must admit I'm glad it was you who was asked this in an interview and not me.