The function $l(s)=0.046 s^{2}-.199 s+.264$ relates the length $(l)$ of a skid mark measured in feet at an accident scene to the speed $(s)$ of the car in miles per hour. That means an accident reconstructionist can measure the length of a skid mark and find the speed the car was traveling. If a skid mark with a length of $82.5 \mathrm{ft}$ was found, find the speed of the car. Round your answer to the nearest tenth.

Step 1 ：We are given the function \(l(s)=0.046 s^{2}-.199 s+.264\) which relates the length \(l\) of a skid mark measured in feet at an accident scene to the speed \(s\) of the car in miles per hour. We are asked to find the speed of the car given that the length of the skid mark is 82.5 feet.

Step 2 ：To find the speed, we need to solve the equation \(l(s)=0.046 s^{2}-.199 s+.264 = 82.5\) for \(s\). This is a quadratic equation, so we can use the quadratic formula to solve for \(s\). The quadratic formula is \(s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation.

Step 3 ：In this case, \(a = 0.046\), \(b = -0.199\), and \(c = 0.264 - 82.5\).

Step 4 ：We calculate the discriminant \(D = b^2 - 4ac = 15.171025\).

Step 5 ：We then calculate the two possible values for \(s\): \(s1 = \frac{-b + \sqrt{D}}{2a} = 44.50000000000001\) and \(s2 = \frac{-b - \sqrt{D}}{2a} = -40.173913043478265\).

Step 6 ：Since the speed of the car cannot be negative, we discard \(s2\) and take \(s = 44.5\) as the solution.

Step 7 ：Final Answer: The speed of the car was approximately \(\boxed{44.5}\) miles per hour.