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 10°F
.
City B is warmer by 10 degrees F .

City B is warmer by 2°F
.
City B is warmer by 2 degrees F .

City A is warmer by 2°F
.
City A is warmer by 2 degrees F .

City A is warmer by 10°F
.
City A is warmer by 10 degrees F .
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1 answer

To determine which city is warmer after 5 hours and the difference in their temperatures, we can calculate the temperatures of both City A and City B after 5 hours.

City A:

  • Initial temperature: 70°F
  • Rate of change: -5°F per hour
  • Change in temperature after 5 hours: \( -5°F \times 5 , \text{hours} = -25°F \)
  • Temperature after 5 hours: \( 70°F - 25°F = 45°F \)

City B:

  • Initial temperature: 70°F
  • Rate of change: -3°F per hour
  • Change in temperature after 5 hours: \( -3°F \times 5 , \text{hours} = -15°F \)
  • Temperature after 5 hours: \( 70°F - 15°F = 55°F \)

Now, comparing the two temperatures after 5 hours:

  • City A: 45°F
  • City B: 55°F

City B is warmer. To find the difference in temperatures:

  • Difference: \( 55°F - 45°F = 10°F \)

So, the final answer is: City B is warmer by 10°F.