Answer:
The number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.
Explanation:
You know that the temperature of liquid at 16.9°C is decreasing at a rate of 2.3°C per minute. Then, the temperature of the liquid after t minutes, as its value decreases, will be the difference between the initial temperature of 16.9 ° C and the temperature after t minutes. So:
temperature of the liquid= 16.9°C - 2.3 °C/minute * t
On the other side, you know that the temperature of a solid at 30.7°C is decreasing at a rate of 6.9°C per minute. Then, the temperature of the solid after t minutes, as its value decreases, will be the difference between the initial temperature of 30.7°C and the temperature after t minutes. So:
temperature of the solid= 30.7°C - 6.9 °C/minute * t
You want to calculate the number of minutes it will take for a liquid and a solid to reach the same temperature. This is:
temperature of the liquid= temperature of the solid
16.9°C - 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t
Solving:
- 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t - 16.9°C
- 2.3 °C/minute * t + 6.9 °C/minute *t= 30.7°C - 16.9°C
4.6 °C/minute * t = 13.8 °C
t=3 minutes
So the number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.