### Petrol Prices

Weekly Problem 28 - 2009
How much does $u$ litres of unleaded cost in terms of the cost per litre of 4 star petrol?

# Roman Distances

##### Stage: 3 Short Challenge Level:

\begin{eqnarray} 8 \; stadia &=& 8 \times 125 \; passus \\ &=& 8 \times 125 \times 5 \; pedes\\ &=& 5000 \; pedes \end{eqnarray}

So Marcus has to walk $5000 \; pedes$. $1$ circuit of his atrium is $50 \times 4 = 200 \; pedes$ long, so he has to walk round his atrium $\frac{5000}{200}=25$ times.

In Roman numerals, $25$ is XXV.

This problem is taken from the UKMT Mathematical Challenges.