Q. 8.134 - Intermediate Algebra

Question

The skid marks of a vehicle involved in an accident were $122$ feet long. Use the formula $s=\sqrt{24d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth. 

Step-by-Step Solution

Answer

The speed of the vehicle before the brakes was applied is $54.1$ miles per hour.

Step 1. Identify and name what we are looking for

It is given that the length of the skid marks is $122$ feet.

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

Let $s$ represents the required speed.

Step 2. Form the equations

The length of the skid marks is $122$ feet. So the equation is $d=122 ...\left(1\right)$

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

Step 3. Solve using substitution

Using the first equation substitute $122$ for $d$ in the second equation and solve for $s$.

$$\begin{gathered} s=\sqrt{24d} \\ s=\sqrt{24·122} \\ s=\sqrt{2928} \\ s\approx 54.1 \end{gathered}$$

Step 4. Check the solution

Substitute $122$ for $d$ and $54.1$  for $s$ in the original equation.

$\begin{array}{rcl}s& =& \sqrt{24d}\\ 54.1& =& \sqrt{24·122}\\ 54.1& =& \sqrt{2928}\\ 54.1& \approx & 54.1\end{array}$

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