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.

A
The temperature at 12:00 a.m. was 57 degrees Fahrenheit.

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

C
The temperature at 12:00 a.m. was 63 degrees Fahrenheit.

D
The temperature is decreasing at a rate of 3 degrees Fahrenheit per hour.

E
The temperature is decreasing at a rate of 9 degrees Fahrenheit per hour.

F
The temperature is decreasing at a rate of 11 degrees Fahrenheit per hour.

1 answer

D and C are the two correct statements.

Here's the method to solve the problem:

Let the temperature at 12:00 a.m. be T.

From 12:00 a.m. to 2:00 a.m., i.e., in 2 hours, the temperature decreased by (T - 54) degrees Fahrenheit.

From 12:00 a.m. to 5:00 a.m., i.e., in 5 hours, the temperature decreased by (T - 45) degrees Fahrenheit.

Since the temperature is decreasing at a constant rate, we can say that the temperature decreased by the same amount in each of these time intervals.

Therefore, (T - 54) / 2 = (T - 45) / 5

On solving this equation, we get T = 63.

So, the temperature at 12:00 a.m. was 63 degrees Fahrenheit.

And, the temperature is decreasing at a rate of (54 - 45) / (5 - 2) = 3 degrees Fahrenheit per hour.