6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{8c9bce2c-4156-4bf6-8d02-9e01d6f11948-07_1052_1447_212_310}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

Figure 4 represents a network of roads. The number on each arc represents the time taken, in minutes, to drive along the corresponding road.

Stieg wishes to minimise the time spent driving from his home at A , to his office at H . The amount of traffic on two of the roads leading into H varies each day, and so the length of time taken to drive along these roads is expressed in terms of $x$, where $x > 7$
\begin{enumerate}[label=(\alph*)]
\item Use Dijkstra's algorithm to find the possible routes that minimise the driving time from A to H . State the length of each route, leaving your answer in terms of $x$ where necessary.\\
(7)

On a particular day, the quickest route from A to H via G is 2 minutes quicker than the quickest route from A to H via E .
\item Calculate the value of $x$. You must make your method and working clear.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2017 Q6 [9]}}