The total average velocity

(I assume west as positive direction) is given by the total displacement, S, divided by the total time taken, t:

where:
-The total displacement S is the algebraic sum of the displacement in the first part of the motion (

, due west) and of the displacement in the second part of the motion (

, due east).
-The total time taken t is the time taken for the first part of the motion,

, and the time taken for the second part of the motion,

.

can be found by using the average velocity and the displacement of the first part:


, instead, can be written as

, where

is the average velocity of the second part of the motion (with a negative sign, since it is due east).
Therefore, we can rewrite the initial equation as:

And by solving it, we find the displacement in the second part of the motion (i.e. how far did the backpacker move east):