Question

The temperature of one furnace is 1,500ºC and cools at a rate of 4.5ºC per minute. The temperature of another furnace is 1200ºC and is heated at a rate of 1.5ºC per minute.

After how many minutes will the furnaces be the same temperature?

Answer 1

Explanation:

To determine when the two furnaces will have the same temperature, you can set up equations for the temperatures of both furnaces over time. Let's denote the time in minutes as "t."

For the first furnace (cooling at a rate of 4.5ºC per minute), you can use the following equation:

Temperature of the first furnace (T1) at time t = 1500ºC - 4.5ºC * t

For the second furnace (heated at a rate of 1.5ºC per minute), you can use this equation:

Temperature of the second furnace (T2) at time t = 1200ºC + 1.5ºC * t

To find when the two furnaces have the same temperature, set T1 equal to T2 and solve for t:

1500 - 4.5t = 1200 + 1.5t

Now, solve for t:

1500 - 1200 = 4.5t + 1.5t

300 = 6t

t = 300 / 6

t = 50

So, the two furnaces will have the same temperature after 50 minutes.

Is this conversation helpful so far?