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.
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.
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.
Now let me share some fun facts about temperature changes. Did you know that the Earth's temperature changes more than a politician's promises during an election campaign? And just like trying to predict the weather, trying to predict a politician's next move is equally as challenging!
To determine the correct statements, we need to analyze the given information:
From 12:00 a.m. to 2:00 a.m., the temperature decreased by 54 - 45 = 9 degrees Fahrenheit.
From 12:00 a.m. to 2:00 a.m., there were 2 hours, so the rate of temperature decrease is 9 degrees Fahrenheit / 2 hours = 4.5 degrees Fahrenheit per hour.
Now let's go through each statement:
A) The temperature at 12:00 a.m. was 57 degrees Fahrenheit. Incorrect. We don't have enough information to determine the temperature at 12:00 a.m.
B) The temperature at 12:00 a.m. was 60 degrees Fahrenheit. Incorrect. We don't have enough information to determine the temperature at 12:00 a.m.
C) The temperature at 12:00 a.m. was 63 degrees Fahrenheit. Incorrect. We don't have enough information to determine the temperature at 12:00 a.m.
D) The temperature is decreasing at a rate of 3 degrees Fahrenheit per hour. Incorrect. The temperature is decreasing at a rate of 4.5 degrees Fahrenheit per hour, not 3 degrees Fahrenheit per hour.
E) The temperature is decreasing at a rate of 9 degrees Fahrenheit per hour. Incorrect. The temperature decreased by 9 degrees Fahrenheit over 2 hours, so the rate of decrease is 4.5 degrees Fahrenheit per hour, not 9 degrees Fahrenheit per hour.
F) The temperature is decreasing at a rate of 11 degrees Fahrenheit per hour. Incorrect. The temperature decreased by 9 degrees Fahrenheit over 2 hours, so the rate of decrease is 4.5 degrees Fahrenheit per hour, not 11 degrees Fahrenheit per hour.
Therefore, the correct statements are D) The temperature is decreasing at a rate of 4.5 degrees Fahrenheit per hour and E) The temperature is decreasing at a rate of 9 degrees Fahrenheit per hour.
To answer this question, we can use the information given and the concept of a constant rate of temperature decrease.
First, we need to find the rate at which the temperature is decreasing. We can do this by finding the difference in temperature between two known times and dividing it by the number of hours between the two times.
Given:
Temperature at 2:00 a.m. = 54 degrees Fahrenheit
Temperature at 5:00 a.m. = 45 degrees Fahrenheit
Time interval = 5:00 a.m. - 2:00 a.m. = 3 hours
Temperature difference = 54 degrees Fahrenheit - 45 degrees Fahrenheit = 9 degrees Fahrenheit
Rate of temperature decrease = Temperature difference / Time interval = 9 degrees Fahrenheit / 3 hours = 3 degrees Fahrenheit per hour
Now, let's analyze the given statements:
A) The temperature at 12:00 a.m. was 57 degrees Fahrenheit.
To determine if this statement is correct, we need to calculate the temperature at 12:00 a.m. by subtracting the rate of temperature decrease over the elapsed time from the temperature at 2:00 a.m.
Temperature at 12:00 a.m. = 54 degrees Fahrenheit - (3 degrees Fahrenheit per hour × 2 hours) = 54 degrees Fahrenheit - 6 degrees Fahrenheit = 48 degrees Fahrenheit
So, statement A is incorrect.
B) The temperature at 12:00 a.m. was 60 degrees Fahrenheit.
Using the same calculation as above:
Temperature at 12:00 a.m. = 54 degrees Fahrenheit - (3 degrees Fahrenheit per hour × 2 hours) = 54 degrees Fahrenheit - 6 degrees Fahrenheit = 48 degrees Fahrenheit
So, statement B is incorrect.
C) The temperature at 12:00 a.m. was 63 degrees Fahrenheit.
Using the same calculation as above:
Temperature at 12:00 a.m. = 54 degrees Fahrenheit - (3 degrees Fahrenheit per hour × 2 hours) = 54 degrees Fahrenheit - 6 degrees Fahrenheit = 48 degrees Fahrenheit
So, statement C is incorrect.
D) The temperature is decreasing at a rate of 3 degrees Fahrenheit per hour.
We already calculated this rate earlier. It is correct.
So, statement D is correct.
E) The temperature is decreasing at a rate of 9 degrees Fahrenheit per hour.
The rate of temperature decrease we calculated earlier is 3 degrees Fahrenheit per hour, not 9.
So, statement E is incorrect.
F) The temperature is decreasing at a rate of 11 degrees Fahrenheit per hour.
We haven't calculated any rate of temperature decrease that is equal to 11 degrees Fahrenheit per hour.
So, statement F is incorrect.
In summary, the correct statements are D) The temperature is decreasing at a rate of 3 degrees Fahrenheit per hour, and all other statements are incorrect.