My Ariens Riding mower is hard to start and quits after 10 mins of mowing?

My Ariens riding mower is hard to start. I pour a little gas in carb and it starts. After I get it started and start to mow, it suddenly stops after about 10 min. I let it cool off and then it starts up no problem. I then mow for 5 min and then it suddenly stops again.