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Question
Question 5
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?
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?
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Solution
Initial temperature i.e., at 12 noon = 10∘C
Change in temperature per hour = −2∘C
Temperature at 1:00 PM = 10∘C+(−2∘C)=8∘C
Temperature at 2:00 PM = 8∘C+(−2∘C)=6∘C
Temperature at 3:00 PM = 6∘C+(−2∘C)=4∘C
Temperature at 4:00 PM = 4∘C+(−2∘C)=2∘C
Temperature at 5:00 PM = 2∘C+(−2∘C)=0∘C
Temperature at 6:00 PM = 0∘C+(−2∘C)=−2∘C
Temperature at 7:00 PM = −2∘C+(−2∘C)=−4∘C
Temperature at 8:00 PM = −4∘C+(−2∘C)=−6∘C
Temperature at 9:00 PM = −6∘C+(−2∘C)=−8∘C
Therefore, the temperature will be 8∘C below zero at 9:00 PM.
It will take 12hours to be midnight(i.e.,12:00 AM) after 12:00 noon.
Change in temperature in 12 hours = −2∘C×12=−24∘C
At midnight, the temperature will be = 10+(-24)
=−14∘C
Therefore, the temperature at midnight will be −14∘C below 0.
Change in temperature per hour = −2∘C
Temperature at 1:00 PM = 10∘C+(−2∘C)=8∘C
Temperature at 2:00 PM = 8∘C+(−2∘C)=6∘C
Temperature at 3:00 PM = 6∘C+(−2∘C)=4∘C
Temperature at 4:00 PM = 4∘C+(−2∘C)=2∘C
Temperature at 5:00 PM = 2∘C+(−2∘C)=0∘C
Temperature at 6:00 PM = 0∘C+(−2∘C)=−2∘C
Temperature at 7:00 PM = −2∘C+(−2∘C)=−4∘C
Temperature at 8:00 PM = −4∘C+(−2∘C)=−6∘C
Temperature at 9:00 PM = −6∘C+(−2∘C)=−8∘C
Therefore, the temperature will be 8∘C below zero at 9:00 PM.
It will take 12hours to be midnight(i.e.,12:00 AM) after 12:00 noon.
Change in temperature in 12 hours = −2∘C×12=−24∘C
At midnight, the temperature will be = 10+(-24)
=−14∘C
Therefore, the temperature at midnight will be −14∘C below 0.
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