In an experiment, the temperature of a liquid at 16.9 degrees Celsius is decreasing at a rate of 2.3 degrees Celsius per minute and the temperature of a solid at 30.7 degrees Celsius is decreasing at a rate of 6.9 degrees Celsius per minute. Enter the number of minutes it will take the liquid and solid to reach the same temperature.
Question
In an experiment, the temperature of a liquid at 16.9 degrees Celsius is decreasing at a rate of 2.3 degrees Celsius per minute and the temperature of a solid at 30.7 degrees Celsius is decreasing at a rate of 6.9 degrees Celsius per minute. Enter the number of minutes it will take the liquid and solid to reach the same temperature.
Solution
To solve this problem, we need to set up an equation that represents the temperatures of the liquid and solid over time.
Let's denote the temperature of the liquid as L and the temperature of the solid as S. The time in minutes will be represented by t.
We know that the liquid starts at 16.9 degrees and is decreasing at a rate of 2.3 degrees per minute. So, the temperature of the liquid at any given time t can be represented as:
L = 16.9 - 2.3t
Similarly, the solid starts at 30.7 degrees and is decreasing at a rate of 6.9 degrees per minute. So, the temperature of the solid at any given time t can be represented as:
S = 30.7 - 6.9t
We want to find the time t when the liquid and solid have the same temperature, so we set L = S and solve for t:
16.9 - 2.3t = 30.7 - 6.9t
Rearranging the terms gives:
6.9t - 2.3t = 30.7 - 16.9
Solving for t gives:
4.6t = 13.8
Finally, dividing both sides by 4.6 gives:
t = 13.8 / 4.6 = 3 minutes
So, it will take 3 minutes for the liquid and solid to reach the same temperature.
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