7. Due to traffic congestion at the city exit, the intercity bus traveled the first third of the journey one and a half times slower than the calculated time. Will the bus be able to arrive at the destination on time if it increases its speed by a third for the remaining part of the journey?
Answer: Yes.

Solution. The bus spent $\frac{3}{2} \cdot \frac{1}{3}=\frac{1}{2}$ of the calculated time on the first third of the journey. If it increases its speed by a third, it will cover the remaining two-thirds of the journey in $\frac{2 / 3}{4 / 3}=\frac{1}{2}$ of the calculated time, meaning it will be able to arrive at the destination without being late.