3 [Figure 1, printed on the insert, is provided for use in part (b) of this question.]
The diagram shows a network of roads. The number on each edge is the length, in kilometres, of the road.
\includegraphics[max width=\textwidth, alt={}, center]{63e7775d-2a63-4584-b3be-ce97927bcfcc-03_716_1303_559_388}

1. 1. Use Prim's algorithm, starting from \(A\), to find a minimum spanning tree for the network.
   2. State the length of your minimum spanning tree.
2. 1. Use Dijkstra's algorithm on Figure 1 to find the shortest distance from \(A\) to \(J\).
   2. A new road, of length \(x \mathrm {~km}\), is built connecting \(I\) to \(J\). The minimum distance from \(A\) to \(J\) is reduced by using this new road. Find, and solve, an inequality for \(x\).