On a road with grade $\displaystyle {G}={0.02}$ and friction coefficient $\displaystyle {f}={0.7}$, the equation for braking distance simplifies from $\displaystyle {d}=\frac{{V}^{{2}}}{{{2}\cdot{32.2}{\left({f}+{G}\right)}}}$ to $\displaystyle {d}=\frac{{V}^{{2}}}{{46.368}}$ where $\displaystyle {V}$ is the initial velocity of the car in feet per second, and $\displaystyle {d}$ is the braking distance in feet.

Suppose there is a car crash. Police can determine from skid marks that the car took 120 feet to brake. Determine the car’s speed when it started braking. Give the speed in miles per hour, rounded to 2 decimal places.

miles per hour

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