Law of conservation of momentum problem

[sidzekrom]

A boat is 4 m long and there is a person standing on one end of it. He walks across to the other end of the boat. The mass of the person is 70 kg and the mass of the boat is 200 kg. Find the distance moved by the boat.
Not very sure of my answer. Need help solving this.

 

[Ken G]

Ask yourself this-- does the center of mass of the person+boat move? Where is that center of mass when the person is at one end of the boat?

 

[sidzekrom]

The problem was actually being solved using the Law of conservation of momentum...
This is what I tried– I took the initial state as that of rest where both the person and the boat possesses a momentum of 0.
I took the velocity of the person as 'v' and that of the boat to be 'u' for the duration of the motion. The velocity of the person relative to an observer on the harbor would be 'v-u' and using this i came up with the equation:
70(v-u)+200u=0
70v-70u+200u=0
70v=-130u
v=(-130/70)u
Multiplying by the time interval 't'
vt=(-130/70)ut
vt=4 (because the length of the boat is 4 m)
4= (-130/70)ut
ut= -4x70/(130)
ut= -2.15
Distance moved by the boat is -2.15 m
I am doubtful about this answer and I would like to know if this approach is correct.