Someone I know just received their black belt in Brazilian jiu-jitsu. It took him ten years, and I'm told this is the typical amount of time it takes in this style. Most martial arts as practiced in the US take about half that time to achieve the coveted black belt. Perhaps BJJ has higher standards or their people want to disassociate with those of the McDojo variety that award black belts at breakneck speed.
There seems to be some controversy over the length of time it should take to get to black belt. (A word to the wise: it's not a good idea to ask "how long will it take to get a black belt" at a traditional school.) Isshinryu karate's Angi Uezu says it takes, on average, about two-and-a-half years on Okinawa. In the All-Japan Karate Federation (formerly, the Zen Nippon Karatedo Renmei), three years is recommended to achieve shodan (1st degree black belt).* It took Chuck Norris fifteen months, kickboxing great Joe Lewis seven months and Isshinryu legend Don Nagle six months to get their black belts while training in Korea or Okinawa during a US military hitch.
Isshinryu's founder, Tatsuo Shimabuku, would grant dan level ranks to certain US servicemen who trained under him rather quickly, knowing it would be years before he would see them again. The Karate Questions and Answers blog has more to say about this. Elsewhere, a Marine who trained under the master in the late fifties recounts that
It took six or seven months to make green belt, and a couple more to make black. He [Shimabuku] didn't give a certificate to Americans until they left Okinawa. At first he gave low grades, but the students persisted until he began to give high grades for a minimum time. One American was given an eighth dan (black belt rank) after only two and a half years in isshin-ryu, while another made seventh dan after one and a half years. To justify such ranks, Shimabuku would say "You'll rate it in 15 or 20 years." He gave higher grades because he thought most Americans would not be returning to Okinawa...
Nevertheless, when the Americans returned to the United States from Okinawa, most did not wait 15 or 20 years, but proclaimed their high grades immediately.
When speaking of the duration of white belt to black belt the only relevance is actual training time in the dojo. One source cites that at least 1000 hours of instruction is required for promotion to 1st dan black belt.† If you train 1 - 1.5 hours per class three times a week, that works out to about five years. Norris, who first took up judo in the Air Force and then switched to tang soo do (a cognate of tae kwon do) while stationed in Korea, would train up to thirty hours per week, about double of what most Americans train in a month. Initially, he didn't even think about getting a black belt. Apparently, he figured out something very important: It's the journey, not the destination, that counts.
* Richard Kim 1974. The Weaponless Warriors. Ohara Publications, Incorporated. †Jennifer Lawler 1996. The Martial Arts Encyclopedia. Masters Press.
It took me three years to reach shodan and I studied nearly every day for 1-2 hours. Sometimes more. I have seen dojo's where it's all about rank, which is unfortunate, but I understand it.
Ultimately a dojo is a small business and needs money and students to function. The majority of new students or the parents of new students seek to have the black belt status. And that's what it is to them a status. But every once in awhile a real student will step into the dojo and they get it. They understand that martial arts encompasses so much more than any belt or rank. Those are the ones that go on to become true martial artists.
That being said, I am very proud of my black belt rank. I worked very hard for three years to achieve it. But I also understand that my belt does not signify the end, it signifies the beginning.
I agree that 1st degree BB signifies a beginning. Speaking from experience the people that stick around the longest tend to teach. Maybe you're doing some instructing already. Something to think about.