Problem 1. Two workers dug a trench in two hours. In the process, the first worker got tired and started working three times slower, while the second worker got more motivated and started working three times faster, so it took them only one hour to lay the second such trench. How many times greater was the productivity of the second worker compared to the first worker initially?
Answer: by $\frac{5}{3}$ times.

Solution. Let the initial productivity of the first worker be $x$, and the productivity of the second worker be $y$. Note that when laying the second trench, the total productivity of the workers was twice as high as the initial productivity, therefore

$$
\begin{gathered}
2(x+y)=\frac{1}{3} x+3 y \\
y=\frac{5}{3} x
\end{gathered}
$$

Thus, the productivity of the second worker was $\frac{5}{3}$ times higher than that of the first worker.

## Criteria

4 p. A complete and justified solution is provided.

In the absence of a correct solution, the highest applicable criterion from those listed below is used:

2 p. A correct equation equivalent to the equation in the solution is formulated, but there is no further progress, or an arithmetic error is made.

1 p. The correct answer is provided, but there is no justification.

0 p. The problem is not solved or is solved incorrectly.