69th Belarusian Mathematical Olympiad

The cyclist went from $A$ to $B$, and after 15 minutes a second cyclist followed him. 27 minutes after the second cyclist's start, the motorcyclist went from $B$ to $A$. All three of them met exactly midway between $A$ and $B$. The motorcyclist turned around when reached $A$, and the second cyclist turned around when reached $B$. After that all three again met at some point. Find the time which the motorcyclist spent to drive from $B$ to $A$.