7.1. $\quad$ A cyclist planned to travel from point $A$ to point $F$ in 5 hours, moving at a constant speed. With the planned speed, he traveled halfway, then increased his speed by $25 \%$. He continued to point $B$ with the new speed. How long did the entire journey take?
Answer: 4 hours 30 minutes. Solution. Let $a$ be the distance between points $A$ and $B$, and $v$ be the planned speed. Then $\frac{a}{v}=5$. The increased speed is $1.25v$. The cyclist will complete the entire journey in $\frac{a}{2v} + \frac{a}{2 \cdot 1.25v} = \frac{4.5}{5} \frac{a}{v} = 4.5$ (hours).