Water temperatures

To 25 liters of water at 50 °C we add 15 liters of water at a different temperature. How many °C should the water be colder than 50 °C so that 40 liters of the water obtained has a temperature 42.5 °C?

Correct answer:

x =  20 °C

Step-by-step explanation:

$$\begin{gathered} V_1=25\text{ l } \\ {t}_1=50\text{ °C } \\ {V}_2=15\text{ l } \\ {t}_3=42.5\text{ °C } \\ {Q}_1+Q_2=Q_3 \\ {m}_1\cdot c\cdot t_1+m_2\cdot c\cdot t_2=m_3\cdot c\cdot t_3 \\ {m}_1\cdot t_1+m_2\cdot t_2=m_3\cdot t_3 \\ \rho \cdot V_1\cdot t_1+\rho \cdot V_2\cdot t_2=\rho \cdot V_3\cdot t_3 \\ {V}_1\cdot t_1+V_2\cdot (50-x)=(V_1+V_2)\cdot t_3 \\ 25\cdot 50+15\cdot (50-x)=(25+15)\cdot 42.5 \\ 15x=300 \\ x=20=20\text{°C} \end{gathered}$$

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