When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round the answers to two decimal place.)
(a) What is the temperature of the drink after 60 minutes?
(b) When will its temperature be 12°C?
To find the temperature of the drink after a certain amount of time, we need to understand how temperature changes over time. In this case, we can assume that the temperature of the drink increases linearly with time.
Let's start with the given information:
Initial temperature (T0) = 5°C
Temperature after 25 minutes (T1) = 10°C
(a) What is the temperature of the drink after 60 minutes?
To find the temperature after 60 minutes, we need to determine the rate of change of temperature.
Rate of change of temperature (R) = (T1 - T0) / (time1 - time0)
R = (10°C - 5°C) / (25 minutes - 0 minutes)
R = 5°C / 25 minutes
R = 0.2°C/minute
Now that we know the rate of change of temperature, we can calculate the temperature after 60 minutes.
Temperature after 60 minutes (T2) = T0 + (R * time2)
T2 = 5°C + (0.2°C/minute * 60 minutes)
T2 = 5°C + 12°C
T2 = 17°C
Therefore, the temperature of the drink after 60 minutes is 17°C.
(b) When will its temperature be 12°C?
To find the time it takes for the drink to reach 12°C, we need to rearrange the equation:
T2 = T0 + (R * time2)
time2 = (T2 - T0) / R
time2 = (12°C - 5°C) / 0.2°C/minute
time2 = 7°C / 0.2°C/minute
time2 = 35 minutes
Therefore, the temperature of the drink will be 12°C after 35 minutes.