How much water with a temperature of 86 degrees is needed in water weighing 500 g

How much water with a temperature of 86 degrees is needed in water weighing 500 g and a temperature of 6 degrees so that the final temperature of the mixture is 36 degrees.

Initial data: t1 (hot water temperature) = 86 ºС; m2 (mass of cold water) = 500 g or 0.5 kg; t2 (cold water temperature) = 6 ºС; tx (steady-state temperature value) = 36 ºС.

Let’s compose the ratio for finding the mass of hot water:

C * m1 * (t1 – tx) = C * m2 * (tx – t2).

m1 * (t1 – tx) = m2 * (tx – t2).

m1 = m2 * (tx – t2) / (t1 – tx).

Let’s perform the calculation:

m1 = 0.5 * (36 – 6) / (86 – 36) = 0.3 kg or 300 g.

Answer: It is necessary to add 300 grams of water at a temperature of 86 ºС.