my new computer is quite fsater than the older one

quite的意思是“相当；完全地”,是一个副词,但它很特殊.它不但能修饰动词、形容词、副词、分词,还能修饰名词、介词短语等.
faster是比较级,一般用much,a little,a bit ,a lot,even,far来修饰比较级