"... quite a ways..."

quite :- adverb
a :- determiner (or definite article)
ways :- noun (plural in form, but used as a singular)
(MWDEU entry on way, link)

An appreciable distance

I am quite a ways from understanding my PC
Belgium is quite a ways from Florida

a fur piece.

I've long used it without giving furlongs a thought.

Thanks, Nuncle. I just couldn't work it out.

Furlong is from Old English furhlang < furh 'furrow, trench' + lang 'long'.