recall your d = rt, distance = rate * time
the rate going south is 13, the rate going east is 10
it took a total amount of 6hours and 72miles for the whole travel
so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles
so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours
thus [tex]\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
South&d&13&t\\
East&72-d&10&6-t
\end{array}
\\\\\\
\begin{cases}
\boxed{d}=13t\\
72-d=10(6-t)\\
----------\\
72-\boxed{13t}=10(6-t)
\end{cases}[/tex]
solve for "t"
so, it travelled East for 6-t hours
