Explanation

(a) If $t_{1}and\ t_{2}$ are the time taken by particle to cover first and second half distance respectively.
$\ \ \ \ \ \ \ \ \ \ \ t_{1} = \frac{x/2}{3} = \frac{x}{6}$
$\ \ \ \ \ \ \ \ \ \ x_{1} = 4.5t_{2}and\ x_{2} = 7.5t_{2}$
So, $x_{1} + x_{2} = \frac{x}{2}$
$\Rightarrow \ \ 4.5t_{2} + 7.5t_{2} = \frac{x}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t_{2} = \frac{x}{24}$
Total time $t = t_{1} + 2t_{2} = \frac{x}{6} + \frac{x}{12} = \frac{x}{4}$
So, average speed = 4 m/s