Alone in your dim, unheated room you light one candle rather than curse the darkness.Disgusted by the mess, you walk directly away from the candle.The temperature (in ${ } ^ { \circ } F$ )and illumination (in % of one candle power)decrease as your distance (in feet)from the candle increases.The table below shows this information. $\begin{array}{ccc}
\text { distance(feet) } & \text { Temp. }(\mathbf{F}) & \begin{array}{c}
\text { illuminatiou } \
(\%)
\end{array} \
0 & 55 & 100 \
1 & 54.5 & 85 \
2 & 53.5 & 75 \
3 & 52 & 67 \
4 & 50 & 60 \
5 & 47 & 56 \
6 & 43.5 & 53
\end{array}$
You are cold when the temperature is below 40°F.You are in the dark when the illumination is at most 50% of one candle power.Suppose you know that at 6 feet the instantaneous rate of change of the temperature is -4.5° F/ft and the instantaneous rate of change of illumination is -3% candle power/ft.Are you in the dark before you are cold, or cold before you are dark?
A)You are cold before you are in the dark.
B)You are in the dark before you are cold.

Question

Alone in your dim, unheated room you light one candle rather than curse the darkness.Disgusted by the mess, you walk directly away from the candle.The temperature (in ${ } ^ { \circ } F$ )and illumination (in % of one candle power)decrease as your distance (in feet)from the candle increases.The table below shows this information. $\begin{array}{ccc}
\text { distance(feet) } & \text { Temp. }(\mathbf{F}) & \begin{array}{c}
\text { illuminatiou } \
(\%)
\end{array} \
0 & 55 & 100 \
1 & 54.5 & 85 \
2 & 53.5 & 75 \
3 & 52 & 67 \
4 & 50 & 60 \
5 & 47 & 56 \
6 & 43.5 & 53
\end{array}$
 You are cold when the temperature is below 40°F.You are in the dark when the illumination is at most 50% of one candle power.Suppose you know that at 6 feet the instantaneous rate of change of the temperature is -4.5° F/ft and the instantaneous rate of change of illumination is -3% candle power/ft.Are you in the dark before you are cold, or cold before you are dark?
A)You are cold before you are in the dark.
B)You are in the dark before you are cold.

Quizplus · Accepted Answer

The temperature decreases to below 40°F at a rate of -4.5°F/ft beyond 6 feet, indicating you would become cold quickly. However, the illumination is already at 53% at 6 feet and decreases at a slower rate of -3% per foot, meaning it would take longer to reach the dark threshold of 50% or less. Therefore, you become cold before you are in the dark.

Alone in Your Dim, Unheated Room You Light One Candle ∘F{ } ^ { \circ } F∘F

Alone in Your Dim, Unheated Room You Light One Candle ${ } ^ { \circ } F$