Answer:
(a)

(b)

Step-by-step explanation:
According to the law of conservation of momentum:

Initially, the girl and the plank are at rest. So, relative to the ice, we have:

(a) The velocity of the girl relative to the ice is:

Here,
is the velocity of the girl relative to the plank and
is the velocity of the plank relative to the ice.
Replacing (1) in (2):

(b) According to (2), the velocity of the plank relative to the surface of ice is:

The negative sing indicates that the plank is moving to the left.