Q. 8.133 - Intermediate Algebra

Question

An accident investigator measured the skid marks of the car. The length of the skid marks was $76$ feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth. 

Step-by-Step Solution

Answer

The speed of the car before the brakes was applied is $42.7$miles per hour.

Step 1. Identify and name what we are looking for

It is given that the length of the skid marks is $76$ feet.

The objective is to find the speed of the car before the brakes was applied.

Let $s$ represents the required speed.

Step 2. Form the equations

The length of the skid marks is $76$ feet. So the equation is $d=76 ...\left(1\right)$

And the formula is given by the equation $s=\sqrt{24d} ...\left(2\right)$

Step 3. Solve using substitution

Using the first equation substitute $76$ for $d$ in the second equation and solve for $s$.

$$\begin{gathered} s=\sqrt{24d} \\ s=\sqrt{24·76} \\ s=\sqrt{1824} \\ s\approx 42.7 \end{gathered}$$

Step 4. Check the solution

Substitute $42.7$ for $s$ and $76$ for $d$ in the second equation.

$\begin{array}{rcl}s& =& \sqrt{24d}\\ 42.7& =& \sqrt{24·76}\\ 42.7& =& \sqrt{1824}\\ 42.7& \approx & 42.708\end{array}$

As the statement is true, so the found solution is correct.