Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 174

Black is in an ice covering on the roads that is especially difficult to see and therefore extremely dangerous for motorists. The distance that a car traveling 30 mph will slide after its brakes are applied is related to the outside temperature by the formula $\displaystyle C = \frac{1}{4} D - 45$, where $C$ is the Celsius temperature and $D$ is the distance in feet that the car will slide.

Determine the distance a car will slide on black ice when the outside temperature is $-3^{\circ} C$.

We solve for $D$ (distance),


$
\begin{equation}
\begin{aligned}

C =& \frac{1}{4} D -45
&& \text{Given equation}
\\
\\
C + 45 =& \frac{1}{4}D
&& \text{Add } 45
\\
\\
4 (C + 45) =& D
&& \text{Multiply both sides by } 4
\\
\\
4C + 180 =& D
&& \text{Apply Distributive Property}
\\
\\
4(-11) + 180 =& D
&& \text{Substitute } C = -11^{\circ}
\\
\\
-44+180 =& D
&& \text{Simplify}
\\
\\
D =& 136 \text{ ft}
&&

\end{aligned}
\end{equation}
$


The car will slide $136$ ft.

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