$(10)$ Chapter $9$ Problem $55.$ A uniform plank of length $5\mathrm{.}4$ m and weight $250$ N rests horizontally on two supports, with $1\mathrm{.}1$ m of the plank hanging over the right support $($see the drawing$).$ To what distance $x($meters$)$ can a person who weighs $420$ N walk on the overhanging part of the plank before it just begins to tip?

Hint: The center of gravity of the plank is in the middle. When the plank just begins to tip, the force exerted on the plank by the left fulcrum is zero.