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?

#### Solution

Initial temperature i.e., at 12 noon = 10°C

Change in temperature per hour = −2°C

Temperature at 1:00 PM = 10ºC + (−2ºC) = 8ºC

Temperature at 2:00 PM = 8ºC + (−2ºC) = 6ºC

Temperature at 3:00 PM = 6ºC + (−2ºC) = 4ºC

Temperature at 4:00 PM = 4ºC + (−2ºC) = 2ºC

Temperature at 5:00 PM = 2ºC + (−2ºC) = 0ºC

Temperature at 6:00 PM = 0ºC + (−2ºC) = −2ºC

Temperature at 7:00 PM = −2ºC + (−2ºC) = −4ºC

Temperature at 8:00 PM = −4ºC + (−2ºC) = −6ºC

Temperature at 9:00 PM = −6ºC + (−2ºC) = −8ºC

Therefore, the temperature will be 8°C below zero at 9:00 PM.

It will take 12 hours to be midnight (i.e., 12:00 AM) after 12:00 noon.

Change in temperature in 12 hours = −2°C × 12 = −24ºC

At midnight, the temperature will be = 10 + (−24)

= −14°C

Therefore, the temperature at midnight will be 14ºC below 0.