A cyclist rides $12km$ east for $24$ minutes, then he turns and heads west for $6$ minutes and $3\mathrm{.}0km.$ Finally, he rides east for $23km,$ which takes $46$ minutes.

Assume the origin of the coordinate system is the cyclist's starting position and the positive $x$ direction is eastward.

a$.$ What is the final displacement of the cyclist?

b$.$ What is his average velocity?