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 2 hours and 40 minutes, without it in 8 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 a third of the total charging time. Give your answer in minutes.
Answer: 288.

Solution. The tablet charges in 160 minutes on fast charging, and in 480 minutes on regular charging. Therefore, on fast charging, $\frac{1}{160}$ of the full charge is completed in 1 minute, and on regular charging, $\frac{1}{480}$ of the full charge is completed in 1 minute. Let $t-$ be the total charging time, then $\frac{t}{3} \cdot \frac{1}{160}+\frac{2 t}{3} \cdot \frac{1}{480}=1$ or $t \cdot \frac{5}{3 \cdot 480}=1$.

We get that $t=\frac{1440}{5}=288$.