Let's solve this step-by-step.
1. Determine the total number of hours from 9 a.m. to 9 p.m.:
- The time interval is from 9 a.m. to 9 p.m., which is 12 hours.
2. Calculate the temperature decrease by 9 p.m.:
- The temperature decreases at a rate of 3 °C per hour.
- Total decrease in temperature over 12 hours is [tex]\( 12 \, \text{hours} \times 3 \, \text{°C/hour} = 36 \, \text{°C} \)[/tex].
3. Determine the temperature at 9 p.m.:
- The temperature at 9 a.m. is 20 °C.
- The temperature at 9 p.m. is [tex]\( 20 \, \text{°C} - 36 \, \text{°C} = -16 \, \text{°C} \)[/tex].
4. Calculate the time when the temperature reaches -10 °C:
- The starting temperature at 9 a.m. is 20 °C.
- We want to find the time when the temperature reaches -10 °C, which is a change of [tex]\( 20 - (-10) = 30 \, \text{°C} \)[/tex].
- The rate of decrease is 3 °C per hour.
- The time required to decrease by 30 °C is [tex]\( \frac{30 \, \text{°C}}{3 \, \text{°C/hour}} = 10 \, \text{hours} \)[/tex].
5. Determine the exact time when the temperature reaches -10 °C:
- The temperature begins to decrease at 9 a.m.
- Adding 10 hours to 9 a.m., we get [tex]\( 9 + 10 = 19 \)[/tex].
- Therefore, the temperature will reach -10 °C at 7 p.m. (or 19:00).
In summary:
- The temperature reaches -10 °C at 7 p.m. (19:00).
- The temperature at 9 p.m. will be -16 °C.
