To determine the time at which the temperature will be 4 °C above zero, given that the temperature at noon is 24 °C and it decreases at a rate of 2 °C per hour, we can follow these steps:
1. Determine the decrease in temperature needed:
- The starting temperature at noon is 24 °C.
- The target temperature is 4 °C.
- Therefore, the decrease in temperature required is:
[tex]\[
24 \, \text{°C} - 4 \, \text{°C} = 20 \, \text{°C}
\][/tex]
2. Calculate the time it takes to decrease the temperature:
- The rate of decrease is 2 °C per hour.
- To find out the time needed to achieve a 20 °C decrease, use the formula:
[tex]\[
\text{Time required} = \frac{\text{Temperature decrease needed}}{\text{Rate of decrease}}
\][/tex]
- Plugging in the numbers, we get:
[tex]\[
\text{Time required} = \frac{20 \, \text{°C}}{2 \, \text{°C per hour}} = 10 \, \text{hours}
\][/tex]
3. Determine the time of day when the target temperature is reached:
- Since the time starts counting from 12 noon, we add the 10 hours to 12 noon:
[tex]\[
12 \, \text{noon} + 10 \, \text{hours} = 10:00 \, \text{PM}
\][/tex]
Additionally, since there are no fractional hours involved in the calculation (0.0 minutes), the exact time remains 10:00 PM sharp.
Therefore, the temperature will be 4 °C above zero at exactly 10:00 PM.
