I would say that you will need a six or seven foot gate. that would be 3 or 3 1/2 feet for each side. The main problem here is sagging of the fence in the center. I suggest to people with this idea to: Put a good size 6 inch wheel on both swinging ends for support of the fence and to have a paved run way for the wheels to roll on. If not, they will bog down in the wet earth.
Then the king posts will need to be heavy duty to support the sideways stress of the weight of the gate. I would suggest here metal oil drilling pipe send down at least four feet in the earth cemented in and counter angle pipe to keep it straight.
So, your simple gate has gone from very simple to very eleborate and the only reason is the width of the gate itself.
I would consider building a simple 36 inch wide gate for the rider mower and then forget the truck idea. this gate size is easily made without any of the above amenities or supports.