What rule applies to who putts first?

I know its common knowledge that furthest out putts first, my question is..is there a rule that states this? I think it's rule 10. The reason I want to know is because the guy I play with takes a long time to putt on purpose so others will get frustrated and putt before him that way he see's the lines. So does rule 10 apply here? Or can we put him on the clock some how?