If you answer there question, or solve the box faster do you get a better item?

I don't believe there is a benefit to answering quickly. The boxes will stack though if you don't answer fast and you only get one reward.

 

 

 

Read more about them here http://www.tip.it/runescape/?page=random_events.htm

Nonono, i don't think so. Because i answer my box after i kill a lesser, takes around 40 seconds and still i get uncut diamond. So i don't think so answering faster helps to get better stuff.