If a man travels at $\frac{1}{x}$ km/h on a journey and returns at $\frac{1}{x^2}$ km/h, then his average speed for the journey is:

$\frac{x+1}{x^2}$ $\frac{2}{x+x^2}$ $\frac{1}{x+x^2}$ $\frac{2x^2}{x+1}$

$\frac{2}{x+x^2}$

Average speed = \(\frac{2 \;×\;speed1\;×\;speed2  }{speed1 \;+\;speed2}\) Average speed = \(\frac{2 \;×\;1/x\;×\;1/x^2  }{1/x \;+\;1/x^2}\) = \(\frac{2   }{x\;+\;x^2}\) The average speed is \(\frac{2   }{x\;+\;x^2}\)