Rate of Change Problem: Cooling in Stages

A piece of molten iron is at \(1200{}^\circ \mathrm{C}\). The temperature of the metal falls at a rate of \(65{}^\circ \mathrm{C}\) per second for the first \(10\) seconds, at a rate of \(30{}^\circ \mathrm{C}\) per second for the next \(8\) seconds and then at a rate of \(3{}^\circ \mathrm{C}\) per second until it reaches room temperature of \(27{}^\circ \mathrm{C}\). Find

1. the temperature of the metal after \(12\) seconds,
2. the total time needed for to reach a temperature of \(27{}^\circ \mathrm{C}\) from \(1200{}^\circ \mathrm{C}\).