Question

Maria is monitoring the temperature of two substances a is currently 96.2 and raising 1.5 each minute substance b is currently 98.5 and cooling 0.8 each minute after how many minutes will the two substances be at the same temperature

Answer 1

1 minute

Explanation:

To determine when the two substances will reach the same temperature, we can set up equations for their temperatures in terms of time (t).

Substance A is currently 96.2 degrees and its temperature is increasing at a rate of 1.5 degrees each minute. Therefore, the equation that models this is:

`\textsf{Temperature of substance A} = 96.2 + 1.5t`

Substance B is currently 98.5 degrees and its temperature is decreasing at a rate of 0.8 degrees each minute. Therefore, the equation that models this is:

`\textsf{Temperature of substance B} = 98.5 - 0.8t`

To determine when the temperatures of the two substances will become equal, simply set the equations equal to each other and solve for t.

`\begin{aligned}96.2 + 1.5t &= 98.5 - 0.8t\\\\96.2 + 1.5t+0.8t &= 98.5 - 0.8t+0.8t\\\\96.2 + 2.3t &= 98.5\\\\96.2 + 2.3t-96.2 &= 98.5-96.2\\\\2.3t &= 2.3\\\\(2.3t)/(2.3)&=(2.3)/(2.3)\\\\t&=1\end{aligned}`

Therefore, substances A and B will be at the same temperature after 1 minute, at which time both substances will be 97.7 degrees.

Answer 2

1 minutes

Explanation:

Definition:

Temperature: A physical quantity that expresses hotness or coldness.

Answer:

In order to find how many minutes it will take for the two substances to be at the same temperature, we can use the following steps:

Set up an equation to represent the temperatures of the two substances over time.

• Substance A: Temperature = 96.2 + 1.5t
• Substance B: Temperature = 98.5 - 0.8t

Set the two temperatures equal to each other to find the time when they will be the same.

`\sf 96.2 + 1.5t = 98.5 - 0.8t`

Subtract 96.2 and add 0.8t on both sides:

`\sf 96.2 + 1.5t-96.2+0.8t = 98.5 - 0.8t-96.2+0.8t`

Simplify:

`\sf 2.3t = 2.3`

Divide both sides by 2.3.

`\sf (2.3t)/(2.3) =( 2.3)/(2.3)`

`\sf t = 1`

Therefore, it will take 1 minute for the two substances to be at the same temperature.