Explanation

(b) Let the total distance travelled by the body is $2S.$ If $t_{1}$ is the time taken by the body to travel first half of the distance, then
${\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t}_{1} = \frac{S}{2}$
Let $t_{2}$ be the time taken by the body for each time interval for the remaining half journey.
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ S = 3t_{2} + 5t_{2} = 8t_{2}$
$So,\ average\ speed\ = \frac{Total\ distance\ travelled}{Total\ time\ taken}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{2S}{t_{1} + 2t_{2}} = \frac{2S}{\frac{S}{2} + \frac{S}{4}} = \frac{8}{3}{ms}^{- 1}$