Aconcagua (22,841' / 6961m) is the highest peak in the Southern and Western Hemispheres, and in fact the highest peak on Earth that is not in Asia.

Cotopaxi (19347' / 5897m) is the second highest peak in Ecuador.

Up & down from Ingreso norte al Parque Nacional Cotopaxi:  (35 km, 2172m ascent)

Charles Raffensperger proposed the challenge (2/16/2015):

Modeled after the South Beyond 6000 (SB6K) I'm planning a similar challenge in Georgia to climb all 4000 or higher peaks in one continuous footpath starting April 3, 2015. There are 32 named peaks along with 3 other "provisional" peaks - I plan to climb all 35. I'll be taking a west-east route and expect the total route will be slightly over 200 miles. To-date there appear to only be 2 other people who have climbed all of these peaks, although not in one continuous trek.