In reaching her destination, a backpacker walks with an average velocity of 1.21

[mytalkingbird]

Homework Statement

In reaching her destination, a backpacker walks with an average velocity of 1.21 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.52 m/s, due west, turns around, and hikes with an average velocity of 0.435 m/s, due east. How far east did she walk? in km? ______km

Homework Equations

The Attempt at a Solution

 

[tvavanasd]

Attempt?

 

[mytalkingbird]

Attempt?

6.44(1000)=(6440m)/(1.21m/s)=(5322.31405seconds)/2.52m/s=2112.029

(6440-d) + ((6440-d)/.435)) = d/1.21

i'm lost. i don't know what to do next.

 

[tvavanasd]

Start by listing all variables that you know. Solve symbolically; it will be too confusing otherwise.
You already know v = x / t and t = x / v
Use and manipulate:
V3 = X3 / T3 (this is average overall)
T3 = T1 + T2
X3 = X1 + X2
You will also need V1 = X1 / T1 and V2 = X2 / T2 (manipulate as necessary).
Solve for Xtotal, then assume that west is positive (east is -ve) and substitute X1 = 6440 m, V1 = 2.52m/s, V3 = 1.21 m/s and V2 = -0.435 m/s

Note that X3 will be her displacement from start to finish, not the total distance that she walked.