Question

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

Answer 1

Hint: Here in this question based on integer concept, the number which is above zero will be considered as a positive number and below zero will be considered as a negative number. To solve this, we have to subtract the temperature of \[{2^ \circ }C\] each hour till it reaches to \[ - {8^ \circ }C\] again by following the same procedure we can determine the temperature at midnight i.e., \[12\] am.

Complete step-by-step answer:
Consider the given, The temperature at 12 noon (12 pm) was \[{10^ \circ }C\] above zero. If it decreases at the rate of \[{2^ \circ }C\] per hour until midnight.
To find: what time would the temperature be \[{8^ \circ }\] C below zero i.e., \[ - {8^ \circ }C\] and What would be the temperature at mid-night i.e., \[12am\] ?
So, the temperature falls from \[{10^ \circ }C\] to \[{0^ \circ }C\] and from \[{0^ \circ }C\] to \[ - {8^ \circ }C\]
Therefore, the total temperature falls is \[{18^ \circ }C\] .
The time taken, to decrease the temperature \[{18^ \circ }C\] at the rate of \[{2^ \circ }C\] is
 \[ \Rightarrow \dfrac{{18}}{2} = 9\] hours.
Initial temperature is 12 noon or 12 pm, so the temperature \[ - {8^ \circ }C\] is
 \[ \Rightarrow 12pm + 9hours\]
 \[ \Rightarrow 9pm\] .
Therefore, the time at which the temperature will be \[ - {8^ \circ }C = 9pm\] .
Now, find the temperature at midnight \[12am\] .
The difference of time from \[9pm\] to \[12am\] is 3 hours.
The temperature falls each hour by \[{2^ \circ }C\] , then
The temperature at 12 am is
 \[ \Rightarrow - {8^ \circ }C + 3\left( { - {2^ \circ }C} \right)\]
 \[ \Rightarrow - {8^ \circ }C - {6^ \circ }C\]
 \[ \Rightarrow - {14^ \circ }C\]
Therefore, at 12 am midnight the temperature will be \[ - {14^ \circ }C\] .

Note: The above question includes the time and temperature, remember the concept the temperature is proportion to the time i.e., when time increases the temperature will vary whether it will increases or decreases and main thing, we have to concentrate on the time i.e., must know when time will be AM or PM.