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?
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 by 55°F - 45°F = 10°F.
To find out which city is warmer after 5 hours, we can calculate the final temperature in each city.
For City A:
Initial temperature = 70°F
Rate of change = -5°F per hour
Time = 5 hours
Using the formula: Final temperature = Initial temperature + (Rate of change * Time)
Final temperature in City A = 70 + (-5 * 5) = 70 - 25 = 45°F
For City B:
Initial temperature = 70°F
Rate of change = -3°F per hour
Time = 5 hours
Final temperature in City B = 70 + (-3 * 5) = 70 - 15 = 55°F
Therefore, the temperature in City B is warmer after 5 hours.
To find the difference in their temperatures after 5 hours, we calculate:
Difference in temperatures = Temperature in City B - Temperature in City A
Difference in temperatures = 55°F - 45°F = 10°F
So, the difference in their temperatures after 5 hours is 10°F.
To find out which city is warmer and the difference in their temperatures after 5 hours, we can calculate the final temperatures in both cities and compare them.
The initial temperature in both City A and City B is 70°F.
In City A, the temperature is changing by −5°F per hour. So, after 5 hours, the change in temperature would be -5°F * 5 = -25°F. Adding this change to the initial temperature of 70°F, we get:
Temperature in City A after 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 change in temperature would be -3°F * 5 = -15°F. Adding this change to the initial temperature of 70°F, we get:
Temperature in City B after 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:
Temperature in City B - Temperature in City A = 55°F - 45°F = 10°F.
Hence, the temperature in City B is 10°F warmer than City A after 5 hours.