A woman who weighs 500N stands on an 8.0-m-long board that weighs 100N. The board is supported at each end. The support force at the right end is 3 times the support force at the left end. How far from the right end is the woman standing?

Answer 1

Let the left end support force be F1 and the right end support force = F2
3F1 = F2 (You are told this)
F1 + F2 = (4/3)F2 = 600 N (From vertical force balance)
F2 = 450 N ; F1 = 150 N
Let the woman's distance from left end = x.
Apply a moment balance. You can apply it anywhere, but chose the left end.

500 x +100*4 = F2*8 = 3600
Complete the solution for x. It will be in meters

Answer 2

1.6