The temperature is shown at 6:00am. It is rising at one degree every thirty minutes. At this rate, it will be 20 degrees at what time?
rate = 1° / 30 min = 2° / 60 min = 2° / h
T = temperature
t = time
Temperature = rate ∙ time
T = rate ∙ t
20 ° = 2° / h ∙ t
t = 20 ° / ( 2° / h )
t = 20 ° ∙ h / 2°
t = 10 h
Reference time = 6:00 am
6:00 am + 10 h = 16 h = 4:00 pm
To find out when the temperature will reach 20 degrees, we need to calculate the number of 30-minute intervals it takes for the temperature to rise from its initial value (shown at 6:00 am) to 20 degrees.
Let's start by determining the temperature increase per hour. Since the temperature is rising at one degree every thirty minutes, it means it will rise by two degrees per hour (1 degree every 30 minutes * 2 = 2 degrees per hour).
To reach 20 degrees, the temperature has to increase by 20 - initial temperature degrees (since we started at 6:00 am). Let's say the initial temperature is T. Then the equation becomes:
20 - T = Temperature increase (in degrees)
Now, let's calculate how many 30-minute intervals it takes for the temperature to increase by (20 - T) degrees. Since the temperature increases by 2 degrees per hour, it increases by one degree every 30 minutes. Therefore, the number of 30-minute intervals can be found by dividing the temperature increase in degrees by 1:
Number of 30-minute intervals = (20 - T) degrees / 1 degree
Simplifying this equation gives us:
Number of 30-minute intervals = 20 - T
So, the temperature will reach 20 degrees after (20 - T) 30-minute intervals. Assuming we start at 6:00 am, we can add (20 - T) 30-minute intervals to 6:00 am to find the time when the temperature will reach 20 degrees.
Therefore, the time when the temperature will be 20 degrees can be calculated as:
6:00 am + (20 - T) 30-minute intervals = Answer
However, to provide an exact time, we'll need to know the initial temperature (T) at 6:00 am.