9.1. The bathtub fills up from the hot water tap in 17 minutes, and from the cold water tap in 11 minutes. After how many minutes from opening the hot water tap should the cold water tap be opened so that by the time the bathtub is full, there is one third more hot water than cold water?
Answer. In 5 minutes.

Solution. Let the volume of the bathtub be $V$, then by the time it is filled, there should be $\frac{3}{7} V$ of cold water and $\frac{4}{7} V$ of hot water in it. The filling rates of cold and hot water are $\frac{V}{11}$ and $\frac{V}{17}$, respectively. Therefore, the desired time is the difference between the time to fill $\frac{4}{7} V$ of the bathtub with hot water and the time to fill $\frac{3}{7} V$ of the bathtub with cold water, that is, $\frac{4}{7} V / \frac{V}{17} - \frac{3}{7} V / \frac{V}{11} = \frac{68 - 33}{7} = 5$ minutes.

Instructions. Answer with verification: 2 points. Formulation of equations: 3 points.