2. The bathtub fills up in 23 minutes from the hot water tap, and in 17 minutes from the cold water tap. Pete first opened the hot water tap. After how many minutes should he open the cold water tap so that by the time the bathtub is full, one and a half times more hot water has been added than cold water?
# 9.2. Answer. In 7 minutes.

In one minute, the hot water tap fills $\frac{1}{23}$ of the bathtub, and the cold water tap fills $\frac{1}{17}$ of the bathtub. After filling the bathtub, the hot water should make up $\frac{3}{5}$ of the bathtub, and the cold water should make up $\frac{2}{5}$ of the bathtub. Therefore, the hot water tap should be open for $\frac{3}{5} / \frac{1}{23} = \frac{69}{5}$ minutes, and the cold water tap should be open for $\frac{2}{5} / \frac{1}{17} = \frac{34}{5}$ minutes. Thus, the cold water tap should be opened $\frac{69}{5} - \frac{34}{5} = 7$ minutes after the hot water tap is opened.

Grading Remarks. If the answer is only guessed, give 0 points. If the answer is guessed and its correctness is neatly verified, give 3 points. If the equation or system is correctly set up but solved with errors, give 4 to 6 points depending on the type of error.