Post your computer specs, And are you doing anything else while you are playing rs or rsps? Do Ctrl + Alt+ Del then go to Processes and print screen that then upload it and post here.
Download CCleaner here: http://ccleaner.software.en.softonic.com/download?gclid=CNum9frWi6YCFQQFbAodEDV8oQ (safe link I promise ). Got it about 2 years ago and it's helped make my comp a lot faster. Basically just cleans out old data you don't need (cookies ect.) and fixes any registry errors for you. Fast dl and very easy to use.
Internet speed / ping is fine. You can run RuneScape perfectly fine with dial up internet as long as your ping is sufficient.
Your problem seems to be with your proccessor, I know how to fix this on a windows system, but on a macbook i would have no clue.
But if your techy enough or have the ability to use google and follow instructions. What you need to search for usually lies within your graphics card options, you will need to low the video render quality.....