A4.5 kg dog stands on an 18 kg flatboat at distance d=6.1 m from the shore. it walks 2.4 m along the boat toward shore and then stops. assuming no friction between the boat and the water, find how far the dog is then from the shore.

If it's a frictionless system with no initial velocity, the center of mass doesn't move. (Conservation of momentum, which = 0 in this case.) As the dog applies to his body the force F needed to reach some speed, the reaction force -F is applied to the boat. With 4 times the dog's mass, the boat moves with 1/4 the acceleration, speed and distance the dog does. So he moves 0.8*2.4 m toward the shore while the boat moves 0.2*2.4 m away from it. His distance is 6.1 - 0.8*2.4 m.