7.4. Katya's hair grows twice as fast as she does, while Alyona, who grows at the speed of Katya's hair, has hair that grows one and a half times faster than Alyona herself. At the present moment, Alyona and Katya have their hair at the same height above the floor. Whose hair will reach the floor first? Justify your answer.
Solution: Let Katya grow by $x$ cm. Then her hair grows by $2 x$ cm and the distance from it to the floor decreases by $2 x - x = x$ cm. During this time, Alyona grows by $2 x$ cm, her hair by $3 x$ cm, and the distance from it to the floor decreases by $3 x - 2 x = x$ cm. Conclusion: Alyona's and Katya's hair will reach the floor simultaneously.

Answer: Simultaneously.

Recommendations for checking:

| is in the work | points |
| :--- | :--- |
| Correct and justified answer | 7 points |
| Answer without justification | 0 points |

![](https://cdn.mathpix.com/cropped/2024_05_06_30cae7e546dcde2db7c2g-3.jpg?height=634&width=606&top_left_y=1892&top_left_x=170)

To the solution of problem 7.5