Asunbather is lying on a floating raft that is stationary. she then gets up and walks to one end of the raft. consider the sunbather and raft as an isolated system.
(a) what is the velocity of the center of mass of this system while she is walking?
(b) does the raft itself move while she is walking? if so, what is the direction of the raft's velocity relative to that of the sunbather?

Explanation:

1.Since initial velocity of the system of the girl and raft is zero, and the there is no external force, the center of mass of system remains stationary

NO.

2 . The center of mass of the system is at rest. So when the person moves towards the end, she applies an opposite force on the boat in the opposite direction, which pushes it backwards. Hence it moves in the direction opposite to that of her movement.

Yes.