Fuel rtz 50 zero turn engine cuts out????

I HAVE A RTZ 50 ZERO TURN FROM 2007 SO IT STARTS UP RUNS GREAT FOR ABOUT 10 MINS THEN CUTS OFF LIKE IT RAN OUT OF GAS BUT STILL HAS GAS IN THE TANK IT WILL TURN OVER AND START BUT WILL NOT STAY ON. IF I LET IT SIT FOR A DAY IT WILL DO THE SAME THING. SO DO U THING i NEED A NEW PUMP OR I HEARD OF FUEL LINES SWELLING UP.