It depends largely on the balance between speed on falling asleep and amount of awareness. If you wake up to perform WBTB, you need to stay up long enough to not be to groggy and with incoherent thoughts, and short enough for not to loose your sleep.

Some people just need 1-5 minutes to be aware, and go back to bed after writing down some notes about their last dream/going to wc. Others need to stay up for a longer time, to organize thoughts, maybe write down their entire last dream. Don't see "aware" as capable of performing mathematical operations only. Aware in the sense that you won't let your mind slip to easily to random thoughts when you're repeating your mantra for example