Question

A 70 kg man stands at the back of a 3.0 meter long boat that has mass 2X kg. The front of the boat is

touching a dock. The man walks to the front of the boat. How far from the dock is he? Assume there is

no friction between the boat and the water.

Answer 1

Boats do not have backs. They have sterns or transoms.
They also have bows.
Anyway:
Find original center of mass from the pier (not a dock but that term is actually often used these days for a pier). I will assume that the center of mass of the boat is 1.5 meters from the pier.

70*3 + 2X*1.5 - (70+2X)Xcg
so
Xcg = (210+ 3X)/(70+2X)
from dock
The Xcg from dock will not change if there are no external forces.
call distance from bow to dock d
[70*d + 2X*(1.5+d)]/(70+2X) = same old Xcg

so
210 + 3X = (70+3X)d + 3 X

d = 210/(70+3X)