The forward speed is about the same for a walk behind and a rider, about 3 mph. The main variable is the width of the mower. Let's say we have a 42" mower. If the overlap is 4", then we have 38" cut.
Then the time to do one acre with a 42" mower is:
220 ft. x 220 ft. / ( 3.17 ft x 4.4 ft/sec x 60 sec/min) = 58 minutes.
You can go faster with a rider, but the quality of cut degrades. The walker gets slower for a large lawn since one gets tired and takes more breaks and tends to slow down on the turns.
I would recommend only a tractor that had a cast iron engine and a rear discharge mower. I had a tractor with an engine with aluminum heads. The first engine failed and I replaced it and the second failed. They both warped and eventually failed. I got a tractor with a cast iron engine and it never quit. Eventually it got so old that when the fuel pump failed, it could not be replaced. Now I am using a WheelHorse/Toro with a 17 HP Kohler 2-cylinder cast iron engine. It is a great machine and has worked flawlessly over 12 seasons. The 17 HP is excessive for mowing or pushing snow, but the 2-cylinder engine is great. I can mow for 5 hours and not get the least bit fatigued. However, with 1-cylinder engines the vibration was so great that my toes and fingers would become numb in less than an hour. I had to take a break every hour to recover.
For the mower, get a steel rear discharge mower. The first mower I got was a cast aluminum mower. Every rock the mower picked up knocked a chunk out of the housing until there was nothing left. Then I got a steel mower, but the aluminum engine gave out and it was not prudent to get a third engine for the steel mower. I did get a tractor with a cast iron engine that could use the steel mower and this combination lasted 20 years.
Now on the WheelHorse/Toro I got a rear discharge mower because it does not throw objects like the side discharge machines. Also, when the grass clippings are too heavy to leave on the ground, I can collect them with a simple sweeper and not need a motorized collection system. Also, it doesn't throw clippings on the flower beds and walks or make passing motorists think they are going to be attacked. It is also easy to mow next to shrubs and trees on either side of the tractor. You don't have to always mow with the discharge to the mowed or unmowed side, depending upon what you are trying to accomplish.