Question

In maths and computer science (as well as a number of other disciplines), there is an area of study called graph theory. A graph in this context is defined as a set of vertices (the circles you can see in the picture below - also called nodes or points) connected by edges (the lines you can see in the picture below - also called edges or links). Graphs like this can be used to model real world situations, enabling us to calculate things about them (for example a graph representing places like the one below could help us to look at issues such as routing, travel time, and so on). Graph theory can get quite complex mathematically, but can also be used to determine simple things like the location of vehicles in traffic at a particular time. Try the graph puzzle below for a small taste of working with graphs.

Below is a map of the busy New York roads.


The circles with letters represent traffic lights and the lines are roads. Note that some traffic lights are represented by the same letter. One way of driving from traffic lights E to G can be described as E D D F G.

On a busy Monday morning, two taxi drivers drive the following routes:

Yellow : E A B A D B A G B G C B
Blue : H C B A C B C G F B C B
If both taxis leave at the same time and drive to each traffic light at the same pace, how many times do they reach the same traffic light at the same time?
Explain your rationale for the final answer that you submit.

They do not reach any traffic lights at the same time.
Two times
Five times
Six times

Answer 1

They reach the same traffic light at the same time six times.

To find out how many times the yellow and blue taxis reach the same traffic light at the same time, we can analyze their routes and identify intersections. Let's break down each taxi's route:

Yellow Taxi:

E A B A D B A G B G C B

Blue Taxi:

H C B A C B C G F B C B

Now, let's see when they both reach the same traffic light:

At step 3 (B)

At step 4 (A)

At step 6 (B)

At step 8 (G)

At step 10 (B)

At step 11 (C)

So, they reach the same traffic light at the same time six times.