For #1

Recall Newton's 2nd Law:

and the rotational version of Newton's 2nd Law:

Since the plank is in static equilibrium and

So choose a +y direction to be directly upward. A Free Body Diagram shows that there are four forces present: The forces A and B acting directly upward, the weight w of the woman acting directly downward, and the weight W of the plank also acting directly downward. So we know that

where m and M are the mass of the woman and the plank respectively.

Also choose a positive rotation to be in the counterclockwise sense. I am going to choose an "axis of rotation" to be at the point where the reaction force A is operating. (We may chooseanypoint as our axis, since there is no rotation anyway.) We don't know where the CM of the plank is yet, so I'm going to place that at a distance x to the right of the axis of rotation. So

<-- That's "2 meters there as the coefficient of w, etc.

We have three unknowns in these two equations.

Well, pick a new axis of rotation and do it again! I'll now pick the axis at the point where B is acting, with the same rotation convention. So

This gives us the system of equations:

We have three equations in three unknowns (A, B, and x), so we may solve this.

I have to get going. If you have a problem solving the system just post in the thread and someone will help you.

-Dan