7.1 A cyclist planned to travel from point A to point B in 5 hours, moving at a constant speed. He moved at the planned speed until the midpoint of the journey, then decided to increase his speed by $25 \%$. He completed the journey to point B at the new speed. How long did the entire trip take?
7.1 A cyclist planned to travel from point A to point B in 5 hours, moving at a constant speed. He moved at the planned speed until the midpoint of the journey, then decided to increase his speed by $25 \%$. He completed the journey to point B at the new speed. How long did the entire journey take?

Answer: 4 hours 30 minutes. Hint: Let a be the distance between points A and B, v be the planned speed. Then $\frac{\mathrm{a}}{\mathrm{v}}=5$. The increased speed is $1.25 \mathrm{v}$. The entire journey will take $\frac{a}{2 v}+\frac{a}{2 \cdot 1.25 v}=\frac{4.5}{5} \frac{a}{v}=4.5$ (hours).