The breaking distance, $LaTeX: \displaystyle d$ , of a car is proportional to the square of the speed, $LaTeX: \displaystyle r$ . If a car traveling at $LaTeX: \displaystyle 60$ miles per hour can stop in $LaTeX: \displaystyle 162$ feet. What is the stopping distance of a car traveling 36 miles per hour? Round the solution to the nearest foot.

The equation of variation is $LaTeX: \displaystyle d=kr^2$ . Evaluating at the known values and solving for $LaTeX: \displaystyle k$ gives $LaTeX: \displaystyle 162=k(60)^2 \iff k=\frac{9}{200}$ . The model is $LaTeX: \displaystyle d=\frac{9}{200}r$ evaluating at $LaTeX: \displaystyle r=36$ gives $LaTeX: \displaystyle d=\frac{1458}{25}\approx 58$ feet