You want to pour a slab of 40 square feet (so something like 5 by 8) and four inches thick. Let's break it down with numbers:
I'm imagining about 1 bag per square foot, so you want approximately 40 bags (that might be a conservative estimate for 60-lb bags).
You mention a concrete-mixing device which you roll back and forth several feet in order to mix. I'm not convinced, but for now I'll just assume that that product works exactly as described on amazon: "fill it, roll it 10 feet, and then back 10 feet, and you have perfectly mixed concrete".
Now, the TIME LIMIT here is crucial: sakrete says you can wait AT MOST somewhere between 20 minutes and 4 hours between pouring and troweling. So this depends on your climate &etc, but if I were you I would want to pour the 40th bucket of concrete within an hour of pouring the first bucket.
When you figure that you want all this mixing and pouring to take place within the space of an hour or so, and would want to run 40 bags through that mixer, that's about 1 minute per mix. I don't think you could keep up that pace even on the FIRST bag, probably more like 5 to 10 minutes per bag for a single person, right? (include time to lift that completed mix and pour it into place). In order to achieve that pace, you would want two people on the mixer and one running water and smoothing as you go.