This varies a lot depending on the organisation, but it will usually take several decades – most of your life – to do it.
The reason why this varies depending on the organisation is that different Taekwondo organisations have different minimum training times between levels of colour belt and black belt. One organisation may require 1 year of training time between first and second degree black belt, 2 years between second and third, 3 years between third and fourth, and so on, whereas another organisation may require 2 years between first and second, 3 years between second and third, 4 years between third and fourth.
Assuming extremely short required training times – 2 years to first degree black belt, 1 to second, 2 to third, 3 to fourth, 4 to fifth, and then 5 for every level after that – it would take 32 years to get to ninth degree black belt. In most Taekwondo organisations, the required training times are longer than this. It should never take less than 30 years to get to ninth degree black belt (from an absolute beginner).
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If you'd like to learn more about the Korean terminology used in Taekwondo, consider buying this book: Taekwondo Terminology. It contains an extensive dictionary of terms used in Taekwondo, as well as explanations on how to pronounce Korean words, and aspects of Korean grammar.