The Spanish word 'huayco', meaning 'landslide' or 'mudslide', comes from the Quechua word 'wayq'u', which meant 'ravine' or 'gully'. This is one of many words that Spanish borrowed from Quechua, the language of the Inca Empire, as Spanish settlers encountered the challenging terrain and natural phenomena of the Andes mountains. The meaning evolved slightly from referring to the geographical feature (a ravine) to describing the dangerous natural event (a landslide) that often occurs in such terrain.

Since 'huayco' comes from Quechua rather than Latin roots, there aren't many common Spanish words that share its etymology. This is typical of Spanish words borrowed from indigenous American languages, which often stand alone in Spanish vocabulary.

There aren't any common English words related to 'huayco', as it comes from Quechua, an indigenous South American language family. English and Spanish share many cognates through their common Indo-European heritage, but words borrowed from Native American languages like this one typically don't have English relatives.