Question

If a person is standing still in a moving elevator at 55 mph what is her speed in mph relative to the elevator

Answer 1

We are standing still inside an elevator

So our speed in the frame of elevator is zero

we can write this relative speed as

$v_{pE} = v_p - v_E$

also we know that speed of the elevator is 55 mph

$v_E = 55 mph$

now the velocity in relative frame is zero as he is  still in the moving elevator while in the ground frame or observing from the ground its velocity will be same as velocity of elevator.

So whenever an object is at rest in a moving frame then its relative velocity with respect to that frame must be ZERO