CPM Homework Help : AC Problem 10-23

A piece of metal at $20°\text{C}$ is warmed at a steady rate of $2$ degrees per minute. At the same time, another piece of metal at $240°\text{C}$ 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.

Hint 1:

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.

Hint 2:

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

Hint 3:

Use substitution to solve the system.

Answer:

$t=44 \text{ minutes}$