Its not really that much of a rewrite. Just add Deltatime code into the loop and multiply everything that moves with your delta variable.
instead of : player.x = player.x + Speed
you write : player.x = player.x + (Speed * delta)
erm.. its been a long time since I've coded.. someone correct me :D
instead of : player.x = player.x + Speed
you write : player.x = player.x + (Speed * delta)
erm.. its been a long time since I've coded.. someone correct me :D