In reaching her destination, a backpacker walks with an average velocity of 1.30 m/s, due west. This average velocity results, because she hikes for 6.22 km with an average velocity of 3.44 m/s due west, turns around, and hikes with an average velocity of 0.321 m/s due east. How far east did she walk (in kilometers)?

To find the distance the backpacker walked east, we need to calculate the total distance she walked west and subtract it from the total distance she traveled.

First, let's calculate the total distance she walked west.
Given:
Average velocity when walking west = 3.44 m/s
Distance when walking west = 6.22 km

We can start by converting the distance from kilometers to meters:
Distance walked west = 6.22 km * 1000 m/km = 6220 m

Now, we can calculate the time it took her to walk west using the formula:
Time = Distance / Velocity
Time taken when walking west = 6220 m / 3.44 m/s ≈ 1808.14 seconds

Since velocity is defined as displacement per unit time, we can calculate the total displacement when walking west using the formula:
Displacement = Velocity * Time
Displacement when walking west = 3.44 m/s * 1808.14 s ≈ 6219.96 m

Next, let's calculate the total distance she traveled during the whole trip, including walking east.
Given:
Average velocity when walking east = 0.321 m/s

Since she is walking east at a slower velocity, we can consider this as slowing down her westward displacement. Thus, the total displacement can be calculated by subtracting her eastward displacement from her westward displacement:
Total displacement = Displacement when walking west - Displacement when walking east
Total displacement = 6219.96 m - (0.321 m/s * 1808.14 s)
Total displacement ≈ 6219.96 m - 581.38394 m
Total displacement ≈ 5638.57606 m

Finally, we can convert the total displacement from meters to kilometers to find the distance she walked east:
Distance walked east = Total displacement / 1000 m/km
Distance walked east ≈ 5638.57606 m / 1000 m/km
Distance walked east ≈ 5.64 km

Therefore, the backpacker walked approximately 5.64 kilometers east.