Question $3\mathrm{.}2(21)$

A cyclist left Town A at $08$:$00$ and traveled to Town B at a speed of $20$ km$/$h throughout the entire journey. A scooter left Town B at $08$:$30$ and traveled toward Town A$.$ The scooter maintained the same speed until it passed the cyclist at $11$:$00.$ The cyclist had covered $4/9$of the journey when they passed each other. The speed of the scooter decreased by $10$ km$/$h after passing the cyclist, and it continued at this new speed for the remainder of the journey.

Question $3\mathrm{.}2\mathrm{.}1(6)$

Find the distance between Town A and Town B$.$