Answer :
Final answer:
To determine when the two substances will be at the same temperature, we set up two equations for their temperatures and solve for the unknown variable, which is the number of minutes. After approximately 1.045 minutes, Substance A and Substance B will be at the same temperature.
Explanation:
To determine when the two substances will be at the same temperature, we need to set up two equations and solve for the unknown variable, which is the number of minutes.
Let's start with Substance A. The temperature is currently 96.2 and rising 1.4 each minute. We can express this as an equation: TA = 96.2 + 1.4t, where TA represents the temperature of Substance A at time t.
Now let's do the same for Substance B. The temperature is currently 98.5 and cooling 0.8 each minute. The equation for Substance B is: TB = 98.5 - 0.8t, where TB represents the temperature of Substance B at time t.
We want to find the time when the temperatures of the two substances are equal, so we set TA equal to TB and solve for t:
96.2 + 1.4t = 98.5 - 0.8t
Combining like terms, we get 2.2t = 2.3 and dividing both sides by 2.2 gives t ≈ 1.045 minutes.
Therefore, after approximately 1.045 minutes, Substance A and Substance B will be at the same temperature.
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It would take 1.045 minutes for both substances to be at the same temperature.
Substance A started at a temperature of 96.2 and is rising at 1.4 every minute. Assuming minutes were denoted as x, the relevant expression would be:
= Starting temperature + (Rate temperature is rising x number of minutes)
= 96.2 + 1.4x
Substance B is reducing in temperature:
= 98.5 - 0.8x
Equate both expressions:
96.2 + 1.4x = 98.5 - 0.8x
1.4x + 0.8x = 98.5 - 96.2
2.2x = 2.3
x = 2.3 / 2.2
= 1.045 minutes
It would therefore take 1.045 minutes for both substances to be at the same temperature.
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