Understanding Newton's Laws of Motion

[Solidmozza]

Hi,
This is more of a problem with concept rather than an actual mathematical problem, so forgive me if I don't use the template provided.

I'm just having an issue with Newtons laws of motion. If I were to pull a box across a floor to the right with my hand, assuming that the mass of the box is 40 kg and the force I use is 20 N, I know mathematically the acceleration is 0.5m/s^2 to the right. However, what happens to the equal and opposite forces? I mean, the box is exerting a force on your hand/body that is equal to 20 N but in opposite direction, but its inertial mass is less than that of my body so the box should still accelerate in my direction, right? But shouldn't the acceleration be less than simply 0.5m/s^2 to the right, because let's say my mass was 80 kg, the acceleration to the left = 0.25m/s^2 and the acceleration to the right is 0.5m/s^2, leaving me with a net acceleration of 0.25m/s^2 to the right? Is it just the frictional force that is combating the force of the box on me that prevents this from happening, and if so, is it just the case that the box doesn't have enough friction to oppose the force of my hand?
Additionally, if this above situation was conducted in a vacuum (me and the box just somewhere in a vacuum, no floor) would the acceleration to the right be 0.25m/s^2?

I know this is probably old hat and is simple stuff, but I appreciate the help!
Thanks

 

[Doc Al]

To understand how an object will accelerate you must know the net force on it. By stipulation, the 20 N force that you exert on the box is the only force acting on the box, so it's the net force on the box. True, the box exerts a 20 N force on your hand. But is that the only force acting on your hand? No.