3. (10 points) A frog starts climbing from the bottom of a 12-meter deep well at 8:00. It climbs up 3 meters and then slides down 1 meter due to the slippery well wall. The time it takes to slide down 1 meter is one-third of the time it takes to climb up 3 meters. At 8:17, the frog reaches 3 meters below the well's mouth for the second time. The time it takes for the frog to climb from the bottom of the well to the mouth is ( ) minutes.
A. 22
B. 20
C. 17
D. 16
【Analysis】The time to slide down 1 meter is 3 times the time to climb up 3 meters; the time to climb 1 meter and slide 1 meter is the same, with climbing 3 meters and sliding 1 meter as one cycle; $(3-1) \times 3+3=9 m$, the frog first climbs to 3 meters away from the well's mouth, (3 - 1) $\times 4+1=9 m$, the frog climbs to 3 meters away from the well's mouth for the second time, at this point, the frog has climbed $(3+1)$ $\times 4+1=17$ meters, which is 4 cycles plus 1 meter, taking 17 minutes, so the frog takes 1 minute to climb $1 \mathrm{~m}$ or slide $1 \mathrm{~m}$; $(12-3) \div(3-1)=4 \cdots 1$, the frog takes 5 cycles to climb from the bottom of the well to the well's mouth, then climbs $2 m$, taking $5 \times(3+1)+2$; solving it will give the answer.

【Solution】Solution: With climbing 3 meters and sliding 1 meter as one cycle; (3 - 1) $\times 3+3=9 m$, the frog first climbs to 3 meters away from the well's mouth, (3 - 1) $\times 4+1=9 m$, the frog climbs to 3 meters away from the well's mouth for the second time, at this point, the frog has climbed 4 cycles plus 1 meter, taking 17 minutes, so the frog takes 1 minute to climb $1 m$ or slide $1 m$; $(12-3) \div(3-1)=4 \cdots 1$, the frog takes 5 cycles to climb from the bottom of the well to the well's mouth, then climbs $2 m$, taking $5 \times(3+1)$ $+2=22$ minutes;

Therefore, the answer is: A.