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 B is warmer by 2°F.
City A is warmer by 2°F.
City B is warmer by 10°F.
City A is warmer by 10°F.
In City A, the temperature is changing by -5°F per hour. Therefore, the change in temperature after 5 hours is -5°F * 5 = -25°F.
In City B, the temperature is changing by -3°F per hour. Therefore, the change in temperature after 5 hours is -3°F * 5 = -15°F.
Both cities started at 70°F, so after 5 hours, the temperature in City A would be 70°F - 25°F = 45°F. The temperature in City B would be 70°F - 15°F = 55°F.
Therefore, City B is warmer by 55°F - 45°F = 10°F. The correct answer is "City B is warmer by 10°F."
To find the difference in temperatures between City A and City B after 5 hours, we need to calculate the change in temperature for each city and then subtract the temperature change in City A from the temperature change in City B.
The temperature change for City A is -5°F per hour, and since there are 5 hours, the total temperature change in City A is -5°F × 5 = -25°F.
The temperature change for City B is -3°F per hour, and since there are 5 hours, the total temperature change in City B is -3°F × 5 = -15°F.
Now, to find the difference in temperatures, we subtract the temperature change in City A from the temperature change in City B: -15°F - (-25°F) = -15°F + 25°F = 10°F.
Since the temperature in both cities started at 70°F, City A is warmer than City B by 10°F.
Therefore, the correct answer is: City A is warmer by 10°F.