Man on a plank- Center of Mass pb.

[Footballer010]

Homework Statement

A man is standing at one end of a plank of length L = 10 m. The man has mass Mman = 100 kg and the plank has mass Mplank = 40 kg and the plank is atop a frictionless sheet of ice. At the other end of the plank sits a large rock of mass Mrock = 200 kg. The center of mass of the man+plank+rock is 6.5 m from the end of the plank where the man is standing.

The man walks to the other end of the plank and sits down on the rock. How far did the plank move along the ice?

Homework Equations

X_cm= m₁x₁+m₂x₂$$\div$$m₁+ m₂

The Attempt at a Solution

SO I added one more mass and plugged in the numbers, solving for X_plank

X_cm= m₁x₁+m₂ x₂+m₃x₃$$\div$$m₁+ m₂+m₃

6.5=((100)(10)+(40)(X_plank)+(200)(0))$$\div$$(340 kg)

And... I wasn't even close. Help

 

[Footballer010]

If it helps... the answer is 2.9 m, but I have no idea why.

 

[rl.bhat]

When man moves forward, to keep the CM constant, the whole plank with man must back. So Man*L = Total mass*x.
Find x.