A bicycle rider covers his onward journey from A to B at 10 km/hr and during the return journey from B to A, he covers the same distance at 8 km/hr. If he finishes the onward and return journey in $4 \frac{1}{2}$ hours, then the total distance covered by him during the entire journey is

Let the distance between A and B be x km.

Time $=\frac{\text { Distance }}{\text { Speed }}$

According to the question,

$\frac{x}{10}+\frac{x}{8}=4 \frac{1}{2}$

$\Rightarrow \frac{4 x+5 x}{40}=\frac{9}{2}$

$\Rightarrow \frac{9 x}{40}=\frac{9}{2} \Rightarrow \frac{x}{40}=\frac{1}{2}$

$\Rightarrow x=\frac{40}{2}=20 \mathrm{~km} .$

∴ Distance covered in whole journey

= 2 × 20 = 40 km