2. (7 points) Cheburashka and Gena ate a cake. Cheburashka ate twice as slowly as Gena, but started eating a minute earlier. In the end, they each got an equal amount of cake. How long would it take Cheburashka to eat the cake alone?
Answer. In 4 minutes.

Solution.

First method. If Cheburashka eats twice as slowly as Gena, then to eat the same amount of cake as Gena, he needs twice as much time. This means that the time Cheburashka ate alone (1 minute) is half of the total time it took him to eat half the cake. Thus, he ate half the cake in 2 minutes, and the whole cake in 4 minutes.

Second method. Let Gena eat the whole cake in $x$ minutes, then Cheburashka needs $2x$ minutes for the whole cake. Each of them got half the cake, so Gena ate for $0.5x$ minutes, and Cheburashka for $x$ minutes. From the condition, it follows that $0.5x + 1 = x$, from which $x = 2$. Therefore, Cheburashka will eat the cake in $2 \cdot 2 = 4$ minutes.

## Grading criteria.

- Any complete correct solution - 7 points.
- The equation is correctly set up and solved, or correct reasoning is provided, but the answer is to a different question - 6 points.
- The solution considers a specific mass of the cake - 2 points.
- The equation is set up correctly but solved incorrectly - 2 points.
- The correct answer is provided, and it is verified that it satisfies the problem's condition - 1 point.
- Only the answer is provided - 0 points.