4 The edges on the network below represent some major roads in a city. The number on each edge is the minimum time taken, in minutes, to drive along that road.
- Use Dijkstra's algorithm on the network to find the shortest possible driving time from \(A\) to \(J\).
- Write down the corresponding route.
- A new ring road is to be constructed connecting \(A\) to \(J\) directly.
Find the maximum length of this new road from \(A\) to \(J\) if the time taken to drive along it, travelling at an average speed of \(90 \mathrm {~km} / \mathrm { h }\), is to be no more than the time found in part (a)(i).
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\section*{(a)(i)}
\includegraphics[max width=\textwidth, alt={}, center]{1258a6d3-558a-46dc-a916-d71f71b175ff-08_912_1276_1053_429}