8. A frog starts climbing out of a 12-meter deep well at 8 o'clock. It climbs up 3 meters and then slides down 1 meter due to the slippery well walls. 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. How many minutes does it take for the frog to climb from the bottom of the well to the mouth of the well?
Analysis: Periodic problem.
The time to slide down 1 meter is three 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 forming one cycle; (3-1) $\times 3+3=9 \mathrm{~m}$, the frog first reaches 3 meters from the well's mouth, (3-1) $\times 4+1=9 \mathrm{~m}$, the frog reaches 3 meters 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 $1 \mathrm{~m}$ 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 $2 \mathrm{~m}$ more, taking $5 \times(3+1)$ $+2=22$ minutes.