# How to remember stopping distances for the Highway Code

The Highway Code makes you learn this complicated table by rote. But it’s significantly less effort to learn the following formulas:

\begin{aligned} s(n) &= \text{stopping distance at } 10n \text{ mph} \\ t(n) &= \text{thinking distance at } 10n \text{ mph} \\ b(n) &= \text{braking distance at } 10n \text{ mph} \\ s(n) &= t(n) + b(n) \\ t(n) &= 3n \text{ meters} \\ b(n) &= \frac{3n^2 + n}{2} - 1 \text{ meters} \\ \end{aligned}

Working through one example, stopping at 60 mph:

\begin{aligned} \text{stopping distance at } 60 \text{ mph} &= s(6) \\ &= t(6) + b(6) \\ &= 18 \text{ meters} + 56 \text{ meters} \\ &= 74 \text{ meters} \\ t(6) &= 3 \times 6 = 18 \text{ meters} \\ b(6) &= \frac{3 \times 6^2 + 6}{2} - 1 = 56 \text{ meters} \\ \end{aligned}

The answer is off by one meter in some cases. But the theory test is multiple-choice, so just pick the answer that’s closest.

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