6 [Figure 1, printed on a separate sheet, is provided for use in this question.]
A theme park is built on two levels. The levels are connected by a staircase. There are five rides on each of the levels. The diagram shows the ten rides: \(A , B , \ldots \ldots J\). The numbers on the edges represent the times, in minutes, taken to travel between pairs of rides.
\includegraphics[max width=\textwidth, alt={}, center]{76bccb26-f2ec-4798-bb6b-89c922f9651a-05_984_1593_584_226}

1. Use Dijkstra's algorithm on Figure 1 to find the minimum time to travel from \(A\) to \(J\).
2. A new staircase is built connecting rides \(B\) and \(G\). The time taken to travel from \(B\) to \(G\) using this staircase is \(x\) minutes, where \(x\) is an integer. The time taken to travel from \(A\) to \(G\) is reduced, but the time taken to travel from \(A\) to \(J\) is not reduced. Find two inequalities for \(x\) and hence state the value of \(x\).
   (4 marks)