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.

Answer 1

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.

Answer 2

The temperature at 12:00 a.m. was 60 degrees Fahrenheit.