Question

Kate has 2 gallons of cold water in a bucket. The temperature of the cold water is 10°C. But Kate wants the water to be at 40°C. So obviously Kate wanted to add some hot water to the bucket. Kate also knows that water from the hot-water tap is at 70°C. How much hot water would Kate add to the cold water in the bucket so that the mixture reaches the comfortable temperature of 40°C?

Answer 1

Let take that Kate will add $x$ gallons of hot water at 70 degrees to 2 gallons of cold water at 10 degrees if she wants to receive warm water at 40 degrees. Than we will have next equation:

$$\begin{array}{l} 70 \cdot x + 10 \cdot 2 = 40 \cdot (2 + x) \Rightarrow \\ \Rightarrow 70 \cdot x + 20 = 80 + 40 \cdot x \Rightarrow \\ \Rightarrow 70 \cdot x - 40 \cdot x = 80 - 20 \Rightarrow \\ \Rightarrow 30 \cdot x = 60 \Rightarrow \\ \Rightarrow x = 2 \\ \end{array}$$

So, she needs to add 2 gallons of hot water for receive warm water.

Answer: 2 gallons.