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(B) Let the total distance be $2d$. The first half distance $d$ is covered with speed $v_1 = 6 \,m/s$.The remaining distance $d$ is covered in two par

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$4$

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(B) Let the total distance be $2d$. The first half distance $d$ is covered with speed $v_1 = 6 \,m/s$.The remaining distance $d$ is covered in two parts,each for time $t$. Let the speeds be $v_2 = 2 \,m/s$ and $v_3 = 4 \,m/s$.For the second half of the journey,the average speed $v'$ is the arithmetic mean of the speeds because the time intervals are equal:$v' = \frac{v_2 + v_3}{2} = \frac{2 + 4}{2} = 3 \,m/s$.Now,the total journey consists of two equal distances $d$ covered with speeds $v_1 = 6 \,m/s$ and $v' = 3 \,m/s$. The average speed for equal distances is given by the harmonic mean:$v_{av} = \frac{2 v_1 v'}{v_1 + v'} = \frac{2 	imes 6 	imes 3}{6 + 3} = \frac{36}{9} = 4 \,m/s$.

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