It can take months. Bears do it every year. Whales do it too.
Bears and whales, I hear, have ENORMOUS stores of fat. Humans don't. Beside, that is part of the bear and whale feeding cycle. It's built into their instinct and cycle of life, isn't it? Bears also SLEEP away the months. They don't NEED so much food for that activity.
It takes an older human (90+ years old) about one month to die when s/he eschews food and only takes liquid. Even if the liquid is all that supplemental stuff to take in lieu of food it's not enough. Of course, one can't predict the EXACT amount of time because so much depends on that person's general health and stamina...and her Maker's will.