How Far East Did the Backpacker Walk?

[Nano-Passion]

Homework Statement

In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due west, turns around, and hikes with an average velocity of 0.447m/s, due east. How far east did she walk?

Homework Equations

The Attempt at a Solution

Okay so I had some help from cramster, but I don't get the last part.

<------------ avg velocity = 1.34m/s
<-------------------- avg velocity = 2.68 m/s & distance = 6440m
-------------> v=.447m/s

Let east be positive direction

1) [avg v = x_w+x_e/t_w+t_e

where t_w is the time spent along the west

2) t_w=x_w/v_w
t_e=x_e/v_e

The step I don't get is when they combine equation (1) and (2) to get

x_e = ((1-v/v_w) x_w) / (1-v/v_e)Please help!

 

[eshaw]

Where did you get the last equation? It is wrong. This is the right expression.

x_{e}=\frac{x_{w}(\frac{v}{v_{w}}-1)}{(1-\frac{v}{v_{e}})}

You get it from combining 1) and 2)