A 55-kg person walks due north with a speed of 1.1 m/s, and her 7.0-kg dog runs directly toward her, moving due south, with a speed of 1.8 m/s.

Answer 1

initial momentum north = 55*1.1-7*1.8

Now I assume she picks the dog up and the system moves on with the same momentum

final momentum north = (55+7)v
so
62 v = 55*1.1 - 7*1.8