Question 10
The road between Town $M$ and Town $S$ is $15$ km long. Anna and Boris both leave Town $M$ at noon, where Anna walks and Boris is riding a bike. Meanwhile, their friend Olga walks starting from Town $S$ to Town $M$ and all three of them are travelling on the same road. When Boris meets Olga, he gives Olga the bike and walks the rest of the way, while Olga travelled by bike until she meets Anna and gives Anna the bike. Anna then bikes the rest of the way, arriving in Town $S$ at the same time as Boris. If the walking speed of each person is $6$ km/h and their biking speed is $15$ km/h, how many hours before noon did Olga leave Town $S$?