Question

the temperature of one furnace is 1,200°c and is cooled at a rate of 15°c per minute. the temperature of another furnace is 900°c and is heated at a rate of 5°c per minute. after how many minutes will the furnaces be the same temperature? enter the answer.

Explanation:

Step1: Set up the equation

Let \(t\) be the number of minutes. The temperature of the first furnace is \(1200 - 15t\). The temperature of the second furnace is \(900+5t\).

Step2: Solve for \(t\)

Set \(1200 - 15t=900 + 5t\).
Add \(15t\) to both sides: \(1200=900 + 20t\).
Subtract \(900\) from both sides: \(300 = 20t\).
Divide both sides by \(20\): \(t=\frac{300}{20}=15\).

Answer:

$15$