Since 12:00 a.m., a cold front has caused the temperature in a particular city to decrease at a constant rate. At 2:00 a.m., the temperature was 54 degrees Fahrenheit, and at 5:00 a.m., the temperature was 45 degrees Fahrenheit. Which of the following statements are correct? Select TWO that apply.
Let the initial temperature at midnight be T, and let the constant rate of decrease be m degrees per hour. Then we have:
- At 2:00 a.m., or 2 hours after midnight, the temperature is T - 2m degrees.
- At 5:00 a.m., or 5 hours after midnight, the temperature is T - 5m degrees.
To find T and m, we can set up a system of equations using the given information:
T - 2m = 54 (equation 1)
T - 5m = 45 (equation 2)
Subtracting equation 2 from equation 1, we get:
3m = 9
m = 3
Substituting m = 3 into either equation, we get:
T - 6 = 54
T = 60
Therefore, the correct statements are:
- The initial temperature at midnight was 60 degrees Fahrenheit.
- The temperature was decreasing at a rate of 3 degrees Fahrenheit per hour.