Answer
$\dfrac{106}{3} \ ft/second$ or, $ 35.333 \ ft/second$
Work Step by Step
The general formula for the average rate of change of distance (S) from $t=3 \ seconds $ to $t=6 \ seconds$ is:
$\dfrac{f(y)-f(x)}{y-x}$
Here, we have: $\dfrac{\triangle s}{\triangle t}=\dfrac{S(6)-S(3)}{6-3}$
or, $=\dfrac{137-31}{3}$
or, $=\dfrac{106}{3}$
or, $=35.333 \ ft/second$