15. (12 points) Xiaohong rests for 10 minutes after every 30 minutes of walking uphill, and rests for 5 minutes after every 30 minutes of walking downhill. It is known that Xiaohong's downhill speed is $1 \frac{1}{2}$ times her uphill speed. If it took her 3 hours and 50 minutes to go uphill, how long did it take her to go downhill?
【Solution】Solution:
$3 \times 60+50=230$ (min)
$230 \div(30+10)=5$ (times) $\cdots 30$ (min)
Rest time on the way up $5 \times 10=50$ (min)
Actual walking time on the way up $230-50=180$ (min)
Actual walking time on the way down $180 \div 1 \frac{1}{2}=120$ (min)
$120 \div 30=4$ (times)
Time taken on the way down $120+(4-1) \times 5=135$ (min)
135 min $=2$ hours 15 min
Answer: It took 2 hours 15 minutes to go down the mountain.