Walking in a Boat (Center of Mass?)

[PrideofPhilly]

Homework Statement

A(n) 64 kg boat that is 8 m in length is initially 8.5 m from the pier. A 32 kg child stands at the end of the boat closest to the pier. The child then notices a turtle on a rock at the far end of the boat and proceeds to walk to the far end of the boat to observe the turtle.

Assume: There is no friction between boat and water.

How far is the child from the pier when she reaches the far end of the boat?

Homework Equations

I am not quite sure if this is a Center of Mass question, but if it is the equation is:

X = m1*x1 + m2*x2/m1 + m2
m = mass
x = distance

The Attempt at a Solution

I really don't know where to begin with this problem. I just need a little push or hint to catalyst the problem solving process.

I understand that when the child is at the far end of the boat he will be 16.5 m away from the pier, but I'm not sure what to do next.

 

[LowlyPion]

Figure that since there is no friction, there is no external force, so the center of mass of both won't change.

Now figure where the center of mass is originally with respect to the center of mass of just the boat. With the child at the other end, how much must the center of mass of the boat shift to account for the change in the position of the child. That distance is how much nearer the pier the boat will move.