### Home > AC > Chapter 10 > Lesson 10.1.2 > Problem10-23

10-23.

A piece of metal at $20°C$ is warmed at a steady rate of $2$ degrees per minute. At the same time, another piece of metal at $240°C$ is cooled at a steady rate of $3$ degrees per minute. After how many minutes is the temperature of each piece of metal the same? Explain how you found your answer.

Define variables.
Let $t=\# \text{ of minutes}$; let $C=\text{ temperature}$ of the metal in $°C$.
Write equations for each metal.
Since the temperatures are changing at constant rates the equations are linear.

Temperature of first piece of metal: $C=20+2t$
Temperature of second piece of metal: $C=240−3t$

Use substitution to solve the system.

$t=44 \text{ minutes}$