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Derek adopted an approach based on a graphical solution and using similar triangles. I have included his graph, for interest, below. I used a graphical approach to solve this problem the first time I met it - and I felt that my solution was quite a neat one.
The last solution, and easily the most elegant, was presented by Ian and Charlie of the William Lovell School. I have added a little to their solution for clarity but it is simple and uses no algebra - quite a surprise and very, very nice as it makes excellent use of proportionality.
What a lovely problem.The negative sign for $y$ has happened because James assumed the second bus was the fastest when it was actually the first bus.
Here is the diagram Derek used for his solution. Although his final answer was wrong, the use of similar triangles can result in a reasonably elegant solution.