Question

The temperature is dropping throughout the day as a cold front comes in. The temperature is changing by -5 Fahrenheit per hour and in city B the temperature is changing by -3 Fahrenheit per hour if the temperature in both cities started at 70 Fahrenheit which city is warmer and what is the difference in their temperatures after five hours.

Answer 1

To determine which city is warmer after five hours, we can calculate the temperature in each city after that time period.

1. **Starting temperature**: Both cities start at 70°F.

2. **Temperature change in City A**:
- Rate of change: -5°F per hour
- After 5 hours:
\[
\text{Temperature in City A} = 70°F + (-5°F \times 5 \text{ hours}) = 70°F - 25°F = 45°F
\]

3. **Temperature change in City B**:
- Rate of change: -3°F per hour
- After 5 hours:
\[
\text{Temperature in City B} = 70°F + (-3°F \times 5 \text{ hours}) = 70°F - 15°F = 55°F
\]

4. **Comparing temperatures**:
- Temperature in City A after 5 hours: 45°F
- Temperature in City B after 5 hours: 55°F

5. **Finding the difference**:
\[
\text{Difference in temperature} = \text{Temperature in City B} - \text{Temperature in City A} = 55°F - 45°F = 10°F
\]

So, after five hours, City B is warmer than City A, and the difference in their temperatures is 10°F.