A mother and her 5-year old daughter are ice skating. While at rest, they face each other then push off each other with their hands, sending them in opposite directions. Assuming the mother weighs much more than the daughter, what motion results?  The mom accelerates faster because she could push with more force.  The little girl accelerates faster because her mom pushed her with more force.  They both accelerate at the same rate because their forces are equal and opposite.  Although the forces are equal and opposite, mom has more inertia. Hence mom

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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”