Position of Center Mass Question

[yb1013]

Homework Statement

Romeo (80.0 kg) entertains Juliet (58.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.80 m away from Juliet, who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on Romeo's cheek. How far does the 85.0 kg boat move toward the shore it is facing?

___________ m

Homework Equations

x_cm = (m1*x1 + m2*x2 + ... ) / (m1 + m2 + ... )

The Attempt at a Solution

Im kind of confused on this problem and really need help..

So far I was trying to figure it out but i think i went the wrong way.. My thinking was that there was no external force on the system, so we could just set two equtions equal to each other.

In doing so i came out with..

Initially, x_cm = [(m_B * L/2) + (m_J * L)] / (m_R + m_B + m_J)

and

Now, x_cm = [ m_B*(d + L/2) + d*(m_R * m_J) ] / [m_R + m_B + m_J]

After setting those equal and solving for d, i came out with .03437m which was the wrong answer..

Can anyone please help me and lead me in the right direction?

 

[yb1013]

nevermind, i somehow got it, not sure i completely understand it, but i will in time =]