Question

On a winter morning, the temperature before sunrise was -11°F. The temperature then rose by 1/2

degree each hour for 7 hours before dropping by 2 1/4
degrees each hour for 3 hours. What was the

temperature, in degrees Fahrenheit, after 10 hours?
A -1 1/4

B -10 1/4

C -14 1/4
D -21 1/4

Answer 1

Let's calculate the temperature step by step.

1. **Initial temperature**: -11°F.

2. **Temperature rise**: The temperature rises by 1/2 degree each hour for 7 hours.
\[
\text{Increase in temperature} = \frac{1}{2} \text{ degrees/hour} \times 7 \text{ hours} = \frac{7}{2} \text{ degrees} = 3.5 \text{ degrees}
\]
So, after 7 hours, the temperature is:
\[
-11 + 3.5 = -7.5°F
\]

3. **Temperature drop**: The temperature drops by 2 1/4 degrees each hour for 3 hours.
First, convert 2 1/4 degrees to an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ degrees}
\]
Now calculate the total drop in temperature:
\[
\text{Drop in temperature} = \frac{9}{4} \text{ degrees/hour} \times 3 \text{ hours} = \frac{27}{4} \text{ degrees} = 6.75 \text{ degrees}
\]
Now, subtract this drop from the temperature after 7 hours:
\[
-7.5 - 6.75 = -14.25°F
\]

So, the final temperature after 10 hours is:
\[
-14.25°F = -14 \frac{1}{4} °F
\]

Thus, the answer is **C -14 1/4**.