Help! Physics Question with average velocity and finding distances ?

Question

In reaching her destination, a backpacker walks with an average velocity of 1.49 m/s, due west. This average velocity results, because she hikes for 5.99 km with an average velocity of 2.67 m/s due west, turns around, and hikes with an average velocity of 0.626 m/s due east. How far east did she walk (in kilometers)?

Answer 1

average velocity = net distance / total time

net distance = distance west - distance east

total time = time west + time east

distance west = 5.99 km

time west = distance west / velocity west

distance east = velocity east x time east

You are given the average velocity, the velocity east, the velocity west, as well as the distance west. So you only have two unknowns: time east and distance east and you have two equations:

You can simplify to:

Dw - De = (Tw + Te) Va

De = Ve Te

so

Dw - Ve Te = Tw Va + Va Te, an equation in one unknown, Te