While playing minecraft there are two things you can do that should speed up the game remarcably. One is that you change the "Render distance" from far to either normal or even lower then that. And the other is that you change the "graphics" option from fancy to fast.
But there are also ways to make the game run smoother with options on your computer and clearing some more RAM up for use.
What I do is I hit ctrl + alt + delete, you open the task manager. You click on the tab called processes, here you should have a long list of processes that the computer are currantly running, right click on the one called javaw.exe, move the cursor to "select prioroty" and change it from normal to high.
And least but not last you could use a software program to free up some extra RAM memory for your computer to use. What it does is that it will close some programs that are running in the background that you won't have to use while playing anyway!
I am using a software called Game Booster, really simple to use, you run the program hit one button and you are done! Game Booster can be downloaded from HERE.