2. Bear Big and Bear Small agreed to climb Baiyun Mountain along the same route on the weekend. They started from the foot of the mountain at the same time and immediately went down after reaching the top. Both of their downhill speeds were twice their respective uphill speeds, and Bear Big was faster than Bear Small. After 2 hours of departure, Bear Big and Bear Small met 1600 meters away from the top; when Bear Small reached the top, Bear Big had just descended to the halfway point. How many hours did Bear Big spend from departure to returning to the foot of the mountain?
2.【Answer】Assuming the speed going downhill is the same as the speed going uphill, the distance between the mountain top and the mountain foot is $\mathrm{S}$ meters
(1) $V_{\text {large }}: V_{=}=(S+800):(S-1600)$
(2) $V_{\text {large }}: V_{=}=\left(S+\frac{S}{2} \div 2\right): S=5: 4$
$$
\begin{array}{l}
\therefore(S+800):(S-1600)=5: 4 \\
\therefore V_{\text {large }}=\frac{11200+800}{2}=6000 \mathrm{~m} / \mathrm{h} \\
\therefore 11200 \div 6000+11200 \div(6000 \times 2)=\frac{14}{5} \mathrm{~h}
\end{array}
$$