Question

The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?

Answer 1

(i) The temperature at 12 noon is given as 10°C.
The temperature decreases by 2°C per hour.
Thus, the temperature decreases by 1°C every half hour.
The difference between 10°C above zero and 8°C below zero is:
10-(-8)=10+8=18°c
The temperature decreases by 18°C over:
\(\frac{18}{2}=9\) hours
Therefore, it takes 9 hours for the temperature to drop from 10°C above zero to 8°C below zero.
Adding 9 hours to 12 noon:
12 noon+9 hours=9 pm
Thus, at 9 pm, the temperature would be 8°C below zero.
(ii) The temperature at 12 noon is 10°C.
The temperature decreases by 2°C each hour.
In 12 hours, the temperature decreases by:
−2°C×12=−24°C
At midnight, the temperature will be:
10°C+(−24°C)=−14°C
Therefore, at midnight, the temperature will be 14°C below zero.