Question

a woman runs 6.2 km south. she then turns around and runs 9.3 km north and then finally turns around once more and runs 4.3 km south. how far and in what direction is she from where she started?

Explanation:

Step1: Calculate net displacement in the north - south direction

South - ward displacements are $6.2$ km and $4.3$ km, north - ward displacement is $9.3$ km. Net south - ward displacement $d_s=(6.2 + 4.3)-9.3$.
$d_s = 10.5 - 9.3=\frac{10.5 - 9.3}{1}=1.2$ km south.

Answer:

She is $1.2$ km south from where she started.