Explanation

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