Is it possible to climb Mount Teide from sea-level in 2 days for a reasonably fit person? Essentially, I was thinking of walking up to the Altavista mountain refuge on the first day (can that be done in about 10 hours walking?) and then up to the summit (and back) on the second day (but probably take a bus back down to sea-level).

PS: I originally asked it on the travel site but was referred to this site as being more appropriate.