to playHow to play arpeggios on piano while keeping right hand steady?

Well, I'm trying to play arpeggios on the left hand on piano while playing the vocals of Iris with the right hand. The problem is, I'm used to my notes being kind of in sync, like when I hit a note with the right hand, I hit a notto playe with the left. How can I keep the arpeggio slow at the right rate while playing the vocals on time? I either slow down the right hand or speed up the left without meaning to.
You should practice on rythym. Try designing an exercito playse using different durations of notes in different hands. For instance try playing an 1/8 note arpeggio in your left hand while playing a quarter note melody in your right and vice versa. Use a metronome if you have one.