Question

©Curriculum Associates, LLC Copying is not permitted. Assessment 2 38 11. On a winter morning, the temperature before sunrise was 211°F. The temperature then rose by 1} 2degree each hour for 7 hours before dropping by 2 1} 4degrees each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours? 햠 21 1} 4햡 210 1} 4햢 214 1} 4햣 221 1}

Answer 1

Let's calculate the temperature step by step.

1. **Initial temperature:** \( 211^\circ F \)

2. **Temperature increase:**
- The temperature rises by \( \frac{1}{2} \) degree each hour for 7 hours.
- Total increase over 7 hours:
\[
7 \times \frac{1}{2} = \frac{7}{2} = 3.5 \text{ degrees}
\]
- Temperature after the increase:
\[
211 + 3.5 = 214.5^\circ F
\]

3. **Temperature decrease:**
- The temperature then drops by \( 2 \frac{1}{4} \) degrees each hour for 3 hours. First, convert \( 2 \frac{1}{4} \) to an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4}
\]
- Total decrease over 3 hours:
\[
3 \times \frac{9}{4} = \frac{27}{4} = 6.75 \text{ degrees}
\]
- Temperature after the decrease:
\[
214.5 - 6.75 = 207.75^\circ F
\]

4. **Final temperature after 10 hours:**
- Convert \( 207.75 \) to a mixed number:
\[
207.75 = 207 + 0.75 = 207 + \frac{3}{4} = 207 \frac{3}{4}
\]

Therefore, the temperature after 10 hours is \( \boxed{207 \frac{3}{4}} \) degrees Fahrenheit.