Money Economy

At the entrance of the house heating system, water of temperature $75^\circ\text{C}$ is supplied at a speed of $15$ liters per minute; at the outlet, water has a temperature of $55^\circ\text{C}.$ With such heating, if the outside temperature were $-10^\circ\text{C},$ the temperature inside the house would be $18^\circ\text{C}.$

After gluing the windows with thermal film, the temperature inside rose to $24^\circ\text{C}.$ Estimate the second-to-second economy of the amount of heat with constant heat exchange conditions, as well as monthly savings of money if you had to use a heat generator at a tariff of $p = \$0.03 \text{/kWh}$ to get the right temperature.

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Details and Assumptions:

• The specific heat of water is $4200\text{ J/(kg } ^\circ\text{C)}.$
• The density of water is $1000\text{ kg/m}^3.$

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Source: All-Ukrainian Olympiad in Physics 2017 (Grade 8, Theoretical tour, #1 by R.V. Martynuk)