GEOMETRY
posted by Twg .
The length of a median of a triangle is 36 units. Describe
the location of the centroid on that median.

All you can say is that the centroid is on the median.
http://www.mathopenref.com/trianglecentroid.html 
The centroid divides the median in the ratio of 2:1, with the longer part towards the vertex.
So your 36 unit median is divided into length of 24 and 12 by the centroid.