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