Average velocity is defined as
[tex]v = \frac{displacement}{time}[/tex]
now we have
when she cross the pool in time t1
[tex]v = \frac{L}{t_1}[/tex]
when she cross the pool back to starting position
[tex]v = - \frac{L}{t_2}[/tex]
Here negative sign is for its return path direction which is reversed of its initial direction.
now for the round trip
displacement = 0
so v = 0