I know it means how long have you been sick? but how does lleva translate
Cuanto tiempo lleva enfermo
in this prhare is the same if you say.. "cuanto tiempo tiene enfermo" (es mas correcto si tu dices asi)
in this pfhare means the same lleva/tiene
tiene/tener = have.
lleva in this sentence means has been "ha estado" Cuanto tiempo ha estado enfermo.
the verb llevar doesnt really translate directly...well it does, but it means a lot of things, or rather, its kind of a vague term used in a lot of ways. it can mean to wear, as in clothes but usually it means 'to carry' in a kind of metaphorical sense. so i think in this case, it kind of means 'how long have you carried the illness for''....sort of, im not a spanish expert but i think thats right. hope that helped.