Unit Rates & Proportions Unit Test
14 of 1514 of 15 Items
Question
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 2°F.
City B is warmer by 10°F.
City A is warmer by 2°F.
City A is warmer by 10°F.
To determine which city is warmer after 5 hours, we need to calculate the temperature change in each city.
In City A, the temperature is changing by -5°F per hour, so after 5 hours, the temperature would decrease by 5*5 = 25°F.
In City B, the temperature is changing by -3°F per hour, so after 5 hours, the temperature would decrease by 3*5 = 15°F.
Since the starting temperature in both cities is 70°F, the final temperature in City A would be 70 - 25 = 45°F, and the final temperature in City B would be 70 - 15 = 55°F.
Therefore, City B is warmer by 55 - 45 = 10°F.
The correct answer is City B is warmer by 10°F.
To find out which city is warmer, we need to calculate the temperature in each city after 5 hours.
In City A, the temperature changes 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 changes 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
Now we can compare the temperatures:
City A: 45°F
City B: 55°F
Since 55°F is higher than 45°F, City B is warmer than City A.
To find the difference in temperatures, we subtract the temperature in City A from the temperature in City B:
55°F - 45°F = 10°F
Therefore, City B is warmer by 10°F. Hence, the correct response is:
City B is warmer by 10°F.
To determine which city is warmer and find the difference in their temperatures after 5 hours, we need to calculate the new temperatures in both cities.
Given:
- Temperature change per hour in City A: -5°F
- Temperature change per hour in City B: -3°F
- Initial temperature in both cities: 70°F
- Duration: 5 hours
To find the new temperature in City A after 5 hours, we need to subtract the temperature change (-5°F) for each hour from the initial temperature (70°F):
New temperature in City A = Initial temperature in City A - (Temperature change per hour in City A x Duration)
= 70°F - (-5°F x 5 hours)
= 70°F + 25°F
= 95°F
To find the new temperature in City B after 5 hours, we follow the same process:
New temperature in City B = Initial temperature in City B - (Temperature change per hour in City B x Duration)
= 70°F - (-3°F x 5 hours)
= 70°F + 15°F
= 85°F
Now that we have calculated the new temperatures in both cities after 5 hours, we can determine which city is warmer and find the difference in their temperatures:
Temperature in City A = 95°F
Temperature in City B = 85°F
The temperature in City A (95°F) is higher than in City B (85°F), so City A is warmer. The difference in their temperatures after 5 hours is 95°F - 85°F = 10°F.
Therefore, the correct response is:
City A is warmer by 10°F.