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 $\text{change} = \text{rate} \times \text{time}$.