Answer
$55.0\ mi, \ 274 \ mi$.
Work Step by Step
Since the shape flown is a parallelogram, then each pair of opposite sides are equal and parallel. So the distance from the NDB station back to the airport will be $55.0\ mi$ and the total distance will be the perimeter of the parallelogram:
$$2(55.0+82.0)=274\ mi. $$
