The temperature at 9 a.m. was 20 °C above zero.
If it decreases at the rate of 3 °C per hour until
9 p.m., at what time would the temperature be
10°C below zero? What would be the temperature
at 9 p.m.?
Answers
Answer:
a) 07:00 PM
b) - 16°C
Step-by-step explanation:
Let's divide the question into 2 parts - a) for finding the time at which the temperature would be at 10°C below zero
and b) for finding the temperature at 09:00 PM
a) Let the time taken in hours for the temperature to reach 10°C below zero, be x
It is given that the decrease in temperature = 3°C per hour
So the temperature went from 20°C above zero to 10°C below zero in x hours
So the temperature went from + 20°C to - 10°C in x hours
Change in temperature = Final temperature - Initial temperature
= - 10 - ( + 20 )
= - 10 - 20
= - 30°C
Change per hour = - 3 °C (Negative sign as the temperature is DECREASING every hour)
Temperature difference = Change of temperature per hour * Time difference
So - 3x = - 30 (Because the change of temperature multiplied the time taken gives us the total change in temperature)
=> x = ( - 30 ) / ( - 3 )
=> x = 10
So it took 10 hours for the temperature to go from + 20°C to - 10°C
The temperature was + 20°C at 09:00 AM
Add 10 to the hours
=> The temperature would be - 10°C at 07:00 PM ( Because 10 hours after 09:00 AM would be 07:00 PM)
b) Now, we are asked what the temperature would be at 09:00 PM
First we must know that time difference between the initial and final reading
So the time difference between 09:00 AM and 09:00 PM is 12 hours
Temperature difference = Change of temperature per hour * Time difference
= - 3 * 12
= - 36°C
So the temperature DECREASED by 36°C from 09:00 AM to 09:00 PM
So the temperature at 09:00 PM (Final temperature) = (Temperature at 09:00 AM -> Initital temperature) + ( Change in temperature)
= + 20 + ( - 36 )
= 20 - 36
= - 16°C
Therefore
a)The time at which the temperature would be 10°C below zero is 07:00 PM
b)The temperature at 09:00 PM would be - 16°C