Brashers is right. A skid sprayer is the way to go. And a spreader for the dry ap rounds. You should be able to do 2000 sqft per minute with a spreader. 2.5 minutes per 5000 sqft lawn--the paperwork probably takes longer.
Do a thousand sqft per minute with a skid sprayer.
And when you do get a ride-on down the road...you can use the skid sprayer to fill up your ride-on. Make some calculations. You just have to deduct whatever weed killer is in the solution, before adding your weed killer to your ride-on tank.