Let us assume, Helen's average speed was v kilometer per hour and the distance between her house and her parent's house is d kilometers.
So, time taken t = d/v hours

Statement 1: No information about d.
So, statement 1 is not sufficient

Statement 2: If her average speed was (v + 8) kmph, she would've taken (t - 1) hours to cover the distance.
So, vt = (v + 8)(t - 1)
So, vt = vt + 8t - v - 8
So, t = (v + 8)/8
As we don't know v, we can't determine t.
So, statement 2 is not sufficient

Both together: t = (v + 8)/8 and v = 72
So, we can find t.
So, both statements together is sufficient

Answer : C