In reaching her destination, a backpacker walks with an average velocity of 1.41 m/s, due west. this average velocity results, because she hikes for 6.30 km with an average velocity of 2.49 m/s due west, turns around, and hikes with an average velocity of 0.630 m/s due east. how far east did she walk (in kilometers)?

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):