1. (17 points) Masha's tablet, which she needed for a presentation at school, was completely drained. Using additional equipment, the tablet can be fully charged in 3 hours, without it in 9 hours. Masha first put the discharged tablet on regular charging, and when she found the equipment, she switched to fast charging and fully charged the tablet. It is known that the tablet charges uniformly both with fast and regular charging. Find the total charging time of the tablet if it was on fast charging for one third of the total charging time. Give your answer in minutes.
Answer: 324.

Solution. The tablet charges in 180 minutes on fast charging, and in 540 minutes on regular charging. Therefore, on fast charging, $\frac{1}{180}$ of the full charge is completed in 1 minute, and on regular charging, $\frac{1}{540}$ of the full charge is completed in 1 minute. Let $t$ be the total charging time, then $\frac{t}{3} \cdot \frac{1}{180}+\frac{2 t}{3} \cdot \frac{1}{540}=1$ or $t \cdot \frac{5}{3 \cdot 540}=1$. We get that $t=\frac{1620}{5}=324$.