need help with distance!?

Question

A uniform plank of length 5.8 m and weight 234 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support. To what distance x can a person who weighs 453 N walk on the overhanging part of the plank before it just begins to tip?

Answer 1

I only took basic statics and never dealt with distributed loads, So i'm going to treat the boards weight as a single point force located in the center of the plank. Setting the left end of the board as point 0, this force will located at x = 5.8/2 = 2.9m. The fulcrum, or right support is at x = 5.8-1.1 = 4.7m. There are two distance D1, and D2, where:

D1 = distance between the boards weight and the right support = 4.7 - 2.9 = 1.8m
D2 = distance from the right support to where the guy is when the board just tips

Conservation of Moment, M, where M=Force*Distance

M(board)=M(dude)

(234N)(D1) = (453N)(D2)

D2 = 234*D1/453 = 234*1.8/453 = 0.93 meters from right support