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 changed 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?
A. City A is warmer by 10°F
B. City A is warmer by 2° F
C. City B is warmer by 10° F
D. City B is warmer by 2° F
In City A, the temperature drops by -5°F per hour, so after 5 hours, the temperature would be 70°F + (-5°F × 5) = 70°F - 25°F = 45°F.
In City B, the temperature drops by -3°F per hour, so after 5 hours, the temperature would be 70°F + (-3°F × 5) = 70°F - 15°F = 55°F.
Therefore, City B is warmer by 10°F.
The correct answer is C. City B is warmer by 10°F.
To determine which city is warmer, we need to compare the temperatures in both cities after 5 hours.
In city A, the temperature is changing by -5°F per hour. Starting at 70°F, after 5 hours, the temperature will have dropped by 5°F × 5 hours = 25°F. Therefore, the temperature in city A after 5 hours will be 70°F - 25°F = 45°F.
In city B, the temperature is changing by -3°F per hour. Starting at 70°F, after 5 hours, the temperature will have dropped by 3°F × 5 hours = 15°F. Therefore, the temperature in city B after 5 hours will be 70°F - 15°F = 55°F.
Thus, the temperature in city B after 5 hours is warmer than city A by 55°F - 45°F = 10°F.
Therefore, the correct answer is:
C. City B is warmer by 10°F.
To determine which city is warmer and calculate the difference in their temperatures after 5 hours, we need to calculate the temperature change in each city and compare the final temperatures.
City A:
Temperature change per hour = -5°F
Temperature change after 5 hours = (-5°F/hour) * 5 hours = -25°F
Final temperature in City A = 70°F + (-25°F) = 45°F
City B:
Temperature change per hour = -3°F
Temperature change after 5 hours = (-3°F/hour) * 5 hours = -15°F
Final temperature in City B = 70°F + (-15°F) = 55°F
Therefore, City A is warmer than City B. To determine the difference in their temperatures, we subtract the temperature of City B from the temperature of City A:
Difference in temperatures = Temperature of City A - Temperature of City B
Difference in temperatures = 45°F - 55°F = -10°F
The correct answer is C. City B is warmer by 10°F.