How many liters of water at 20C and 100C should be mixed to get 100 liters of water at 40C?

Given: t1 (cool water temperature) = 20 ºС; t2 (mass of boiling water) = 100 ºС; V (volume of water obtained) = 100 l; t (required temperature) = 40 ºС.

1) The ratio of water volumes: С * m1 * (t – t1) = C * m2 * (t2 – t).

ρ * V1 * (t – t1) = ρ * V2 * (t2 – t).

V1 * (40 – 20) = V2 * (100 – 40).

20V1 = 60V2.

V1 = 3V2.

2) Volumes of water: V1 + V2 = 100 = 3V2 + V2, whence V2 = 100/4 = 25 liters and V1 = 100 – 25 = 75 liters.

Answer: It is required to mix 75 liters of water at a temperature of 20 ºС and 25 liters of water at a temperature of 100 ºС.