# The temperature of cold and hot water is 12 and 70 ° C, respectively.

**The temperature of cold and hot water is 12 and 70 ° C, respectively. How much cold and hot water does it take to fill the bathtub with water at 37 ° C? The mass of water in the bath is 150 kg.**

tx = 12 ° C.

tg = 70 ° C.

t = 37 ° C.

m = 150 kg.

The amount of thermal energy Q, which hot water will give when mixing, is expressed by the formula: Q = C * mg * (tg – t), where C is the specific heat capacity of water, m is the mass of hot water, tg, t are the final and initial water temperatures.

The amount of thermal energy Q, which cold water will take upon mixing, is expressed by the formula: Q = C * mх * (t – tх), where C is the specific heat capacity of water, mх is the mass of cold water, t, tх are the final and initial water temperatures.

C * mg * (tg – t) = C * mx * (t – tx).

m = mg + mх.

mg = m – mх.

mg * (tg – t) = mх * (t – tх).

(m – mx) * (tg – t) = mx * (t – tx).

m * tg – mх * tg – m * t + mх * t = mх * t – mх * tх.

m * tg – m * t = mх * t – mх * tх + mх * tg – mх * t.

m * tg – m * t = mх * tg – mх * tх.

mx = m * (tg – t) / (tg – tx).

mх = 150 kg * (70 ° С – 37 ° С) / (70 ° С – 12 ° С) = 85.3 kg.

mg = 150 kg – 85.3 kg = 64.7 kg.

Answer: mx = 85.3 kg of cold water and mg = 64.7 kg of hot water were mixed in a bath.