A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour. What was the temperature:
1 hour ago?
3 hours ago?

The problem states that the temperature is falling at a constant rate of 3°C per hour. To find the temperature at a given time before the current moment, we can use the following formula:

\[
T_{\text{past}} = T_{\text{current}} + (\text{rate of change} \times \text{time difference})
\]

where:
- \( T_{\text{past}} \) is the temperature at the time in the past,
- \( T_{\text{current}} = 0°C \) (current temperature),
- Rate of change is \(-3°C\) per hour (since the temperature is decreasing).

### 1 hour ago:
\[
T_{\text{1 hour ago}} = 0°C + (-3°C \times (-1)) = 0°C + 3°C = 3°C
\]

So, the temperature 1 hour ago was **3°C**.

### 3 hours ago:
\[
T_{\text{3 hours ago}} = 0°C + (-3°C \times (-3)) = 0°C + 9°C = 9°C
\]

So, the temperature 3 hours ago was **9°C**.

Would you like more details on this explanation?

### Related Questions:
1. What will the temperature be in 2 hours if the rate continues?
2. How would the formula change if the temperature were increasing?
3. How can we model this situation using a linear equation?
4. If the temperature change was not constant, how would you calculate it?
5. What would the temperature be 5 hours ago?

### Tip:
When dealing with constant rates of change, always use the basic formula \( \text{change} = \text{rate} \times \text{time} \).

A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour. What was the temperature 1 hour ago? 3 hours ago?

Learn how to calculate the temperature 1 hour and 3 hours ago using a constant rate of change. The problem involves basic algebra, linear equations, and rates of temperature drop, making it suitable for Grades 6-8 students.

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