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
After 5 hours, the temperature in City A will be 70°F - (5°F/hour * 5 hours) = 70°F - 25°F = 45°F.
The temperature in City B after 5 hours will be 70°F - (3°F/hour * 5 hours) = 70°F - 15°F = 55°F.
Therefore, City B is warmer than City A after 5 hours, and the difference in their temperatures is 55°F - 45°F = 10°F.
To determine which city is warmer and calculate the temperature difference after 5 hours, we can first calculate the final temperatures in each city after 5 hours.
In City A, the temperature is changing by −5°F per hour for 5 hours:
Final temperature in City A = 70°F + (-5°F/hour * 5 hours)
Final temperature in City A = 70°F + (-25°F)
Final temperature in City A = 70°F - 25°F
Final temperature in City A = 45°F
In City B, the temperature is changing by −3°F per hour for 5 hours:
Final temperature in City B = 70°F + (-3°F/hour * 5 hours)
Final temperature in City B = 70°F + (-15°F)
Final temperature in City B = 70°F - 15°F
Final temperature in City B = 55°F
Comparing the final temperatures, we can see that City A is warmer than City B. The temperature difference after 5 hours is:
Temperature difference = Final temperature in City A - Final temperature in City B
Temperature difference = 45°F - 55°F
Temperature difference = -10°F
Therefore, City A is warmer than City B by 10°F after 5 hours.
To determine which city is warmer and the difference in their temperatures after 5 hours, we need to calculate the temperature change for each city.
In City A, the temperature is changing by -5°F per hour. Therefore, the temperature after 5 hours can be calculated by multiplying the temperature change per hour (-5°F) by the number of hours (5) and subtracting it from the initial temperature of 70°F:
Temperature in City A after 5 hours = 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. Following the same calculation, the temperature in City B after 5 hours is:
Temperature in City B after 5 hours = 70°F - (3°F/hour * 5 hours) = 70°F - 15°F = 55°F
Therefore, the temperature in City A after 5 hours is 45°F, and the temperature in City B after 5 hours is 55°F.
To determine which city is warmer, we compare their temperatures. In this case, City B has a higher temperature after 5 hours (55°F) compared to City A (45°F). Thus, City B is warmer.
The difference in temperature between the two cities after 5 hours can be calculated by subtracting the temperature in City A from the temperature in City B:
Temperature difference after 5 hours = Temperature in City B - Temperature in City A
= 55°F - 45°F
= 10°F
Therefore, the difference in temperature between the two cities after 5 hours is 10°F.