3. In the cottage village where Gavrila spends his summers, there is a water supply with cold water. The boy's parents installed a water heater, which has a fixed power as long as the temperature of the water in it is below $100^{\circ} \mathrm{C}$. After the water pipe enters the house, a tee was installed so that part of the water goes through the heater to the hot tap, and the rest goes directly to the cold tap. Before exiting, the hot and cold water mix. Gavrila fully opened the cold tap and found that the water temperature was $20^{\circ} \mathrm{C}$. When he closed the cold tap and opened the hot one, water with the same flow rate came out at a temperature of $40^{\circ} \mathrm{C}$. Then Gavrila opened both taps equally so that the flow rate remained the same. What is the water temperature in this case?
Solution. In both cases, the same amount of water passes through in the same time with the same flow rate, and the same amount of heat is transferred to it. Therefore, the outlet temperature is the same: $t_{3}=t_{2}=40^{\circ} \mathrm{C}$.

Answer: $40^{\circ} \mathrm{C}$.

Criteria: 20 points - correct solution, possibly through the heat balance equation; 10 points - it is shown that when the flow rate through the heater decreases, the temperature of the hot water increases, but the final temperature is found incorrectly; $\mathbf{0}$ points - everything else.