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 B is warmer by 2°F.
City B is warmer by 2 degrees F .
City B is warmer by 10°F.
City B is warmer by 10 degrees F .
City A is warmer by 2°F.
City A is warmer by 2 degrees F .
City A is warmer by 10°F.
The correct response is: City A is warmer by 2°F.
To determine which city is warmer after 5 hours, we need to calculate the change in temperature for each city.
In City A, the temperature is changing by -5°F per hour. So after 5 hours, the temperature in City A would be:
70°F + (-5°F/hour * 5 hours) = 70°F - 25°F = 45°F
In City B, the temperature is changing by -3°F per hour. So after 5 hours, 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 than City A by 10°F.
To determine which city is warmer and find the difference in their temperatures after 5 hours, we need to calculate the final temperatures in both cities after 5 hours.
We know that the temperature in City A is changing by -5°F per hour, which means it is decreasing by 5°F every hour. So 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 is changing by -3°F per hour, which means it is decreasing by 3°F every hour. So after 5 hours, the temperature in City B would be:
70°F - (3°F/hour * 5 hours) = 70°F - 15°F = 55°F
Now we can compare the final temperatures in both cities.
The temperature in City A after 5 hours is 45°F, while the temperature in City B after 5 hours is 55°F.
Since 55°F is higher than 45°F, we can conclude that City B is warmer.
To find the difference in their temperatures after 5 hours, we subtract the temperature in City A from the temperature in City B:
55°F - 45°F = 10°F
Therefore, the correct answer is "City B is warmer by 10°F."