The temperature is dropping throughout the day as a cold front comes in. In City A, the temperature is changing by −5°F per hour, and in City B the temperature is changing by −3°F per hour. If the temperatures in both cities started at 70°F , which city is warmer, and what is the difference in their temperatures after 5 hours?(1 point)%0D%0AResponses%0D%0A%0D%0ACity A is warmer by 2°F.%0D%0ACity A is warmer by 2 degrees F .%0D%0A%0D%0ACity A is warmer by 10°F.%0D%0ACity A is warmer by 10 degrees F .%0D%0A%0D%0ACity B is warmer by 2°F.%0D%0ACity B is warmer by 2 degrees F .%0D%0A%0D%0ACity B is warmer by 10°F.
City A is warmer by 10°F.
To determine which city is warmer and the difference in their temperatures after 5 hours, we need to calculate the temperatures in both cities at the end of the 5-hour period.
Let's start with City A:
The temperature in City A is changing by -5°F per hour. Since the initial temperature is 70°F, after 5 hours, the temperature will decrease by (5 hours × -5°F/hour) = -25°F.
So, the temperature in City A after 5 hours will be: 70°F + (-25°F) = 45°F.
Now, let's move to City B:
The temperature in City B is changing by -3°F per hour. Using the same approach as above, the temperature in City B after 5 hours will decrease by (5 hours × -3°F/hour) = -15°F.
Thus, the temperature in City B after 5 hours will be: 70°F + (-15°F) = 55°F.
Now, we can compare the temperatures in both cities after 5 hours:
The temperature in City A is 45°F, and the temperature in City B is 55°F.
To determine the difference, we subtract the temperature in City A from the temperature in City B: 55°F - 45°F = 10°F.
Therefore, City B is warmer by 10°F, and the difference in their temperatures after 5 hours is 10°F.