Friction and Max accleration, please explain this example.

[Yay]

Homework Statement

I'm trying to develop an expression for the maximum accerlation of a person pushing an object up a slope. I've figured out an expression for acceleration using F = MA based on the forces acting on the person and the object. Now I need to find the max accerlation.

We were given a very similar example and solution (same situation, expect the person and the object are on a flat surface). This is an assignment, so I don't want to ask for help on the actual question (pretty sure the uni calls that cheating :P), just the similar example, and hopefully someone will be able to explain what is going on.

Homework Equations

A = F1 - U2kMG / (M1 + M2) subscripts are in lower case letters.

F1 is the frictional force of the person walking
Uxk is mu the coffiecent of kientic friction for object x.
MG is the mass * Gravity

M1 and M2 is the mass of the person and the object.

The solution is then goes:
The acceleration will be a maximum when f1 has reached it maximum at limiting
friction as specified above, when

a = ( U1M -U2M / (M1 + M2) )g

The Attempt at a Solution

I'm only asking for an explanation for a example question and answer.

 

[Doc Al]

There are two horizontal forces acting on the system. The static (not kinetic) friction on the man which acts in the forward direction and the kinetic friction on the box which acts in the backward direction. What's the maximum value of static friction? Apply Newton's 2nd law to the "man + box" system.