The total average velocity
![v=+1.41 m/s](https://tex.z-dn.net/?f=v%3D%2B1.41%20m%2Fs)
(I assume west as positive direction) is given by the total displacement, S, divided by the total time taken, t:
![v= \frac{S}{t}= \frac{S_1+S_2}{t_1+t_2}](https://tex.z-dn.net/?f=v%3D%20%5Cfrac%7BS%7D%7Bt%7D%3D%20%5Cfrac%7BS_1%2BS_2%7D%7Bt_1%2Bt_2%7D%20%20)
where:
-The total displacement S is the algebraic sum of the displacement in the first part of the motion (
![S_1=6.30 km=6300 m](https://tex.z-dn.net/?f=S_1%3D6.30%20km%3D6300%20m)
, due west) and of the displacement in the second part of the motion (
![S_2](https://tex.z-dn.net/?f=S_2)
, due east).
-The total time taken t is the time taken for the first part of the motion,
![t_1](https://tex.z-dn.net/?f=t_1)
, and the time taken for the second part of the motion,
![t_2](https://tex.z-dn.net/?f=t_2)
.
![t_1](https://tex.z-dn.net/?f=t_1)
can be found by using the average velocity and the displacement of the first part:
![t_1= \frac{S_1}{v_1}= \frac{6300 m}{2.49 m/s}=2530 s](https://tex.z-dn.net/?f=t_1%3D%20%5Cfrac%7BS_1%7D%7Bv_1%7D%3D%20%5Cfrac%7B6300%20m%7D%7B2.49%20m%2Fs%7D%3D2530%20s%20%20)
![t_2](https://tex.z-dn.net/?f=t_2)
, instead, can be written as
![\frac{S_2}{v_2}](https://tex.z-dn.net/?f=%20%5Cfrac%7BS_2%7D%7Bv_2%7D%20)
, where
![v_2=-0.630 m/s](https://tex.z-dn.net/?f=v_2%3D-0.630%20m%2Fs)
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:
![v=1.41 = \frac{6300+S_2}{2530- \frac{S_2}{0.630} }](https://tex.z-dn.net/?f=v%3D1.41%20%3D%20%5Cfrac%7B6300%2BS_2%7D%7B2530-%20%5Cfrac%7BS_2%7D%7B0.630%7D%20%7D%20)
And by solving it, we find the displacement in the second part of the motion (i.e. how far did the backpacker move east):