[ Work problem. $]$

The bathtub fills up in 23 minutes from the hot water tap, and in 17 minutes from the cold water tap. Masha first turned on the hot water tap. After how many minutes should she turn on the cold water tap so that by the time the bathtub is full, 1.5 times more hot water is used than cold water?
To have 1.5 times more hot water than cold water in the bathtub, the cold water tap should fill 2/5 of the bathtub, and the cold water $-3 / 5$. Then the hot water tap should be open for $3 / 5 \cdot 23=69 / 5$ minutes, and the cold water tap for $2 / 5 \cdot 17=34 / 5$ minutes. Therefore, the cold water tap should be opened after $69 / 5-34 / 5=7$ minutes.

## Answer

After 7 minutes.