Question 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) Responses City A is warmer by 10°F. City A is warmer by 10 degrees F . City B is warmer by 10°F. City B is warmer by 10 degrees F . City B is warmer by 2°F. City B is warmer by 2 degrees F . City A is warmer by 2°F. City A is warmer by 2 degrees F .
After 5 hours, the temperature in City A would be 70°F + (-5°F/hour * 5 hours) = 70°F - 25°F = 45°F.
Similarly, the temperature in City B would be 70°F + (-3°F/hour * 5 hours) = 70°F - 15°F = 55°F.
Therefore, City B is warmer by 10°F.
To find the difference in temperatures after 5 hours, we need to calculate the change in temperature in each city and subtract them from each other.
In City A, the temperature is changing by −5°F per hour. After 5 hours, the temperature would have dropped by 5 * 5 = 25°F.
In City B, the temperature is changing by −3°F per hour. After 5 hours, the temperature would have dropped by 3 * 5 = 15°F.
Since the initial temperature in both cities is 70°F, the final temperature in City A would be 70 - 25 = 45°F, and the final temperature in City B would be 70 - 15 = 55°F.
Therefore, City B is warmer by 55°F - 45°F = 10°F. Hence, the correct answer is:
City B is warmer by 10 degrees F.
To determine which city is warmer after 5 hours and the difference in their temperatures, we need to calculate the temperature in each city after 5 hours.
City A's temperature is changing by -5°F per hour, so after 5 hours, the temperature in City A would decrease by (-5°F per hour) * (5 hours) = -25°F.
City B's temperature is changing by -3°F per hour, so after 5 hours, the temperature in City B would decrease by (-3°F per hour) * (5 hours) = -15°F.
To find the final temperature in each city, we need to subtract the temperature change from the initial temperature of 70°F.
City A's final temperature = 70°F - 25°F = 45°F
City B's final temperature = 70°F - 15°F = 55°F
Therefore, City B is warmer than City A by 10°F (55°F - 45°F).