Question

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 :EABADBAGBGCB Blue :HCBACBCGFBCB 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

After comparing the routes of the two taxis and identifying the points at which they coincide, it can be concluded that the two taxis reach the same traffic light at the same time on five occasions.

Step-by-step explanation:

We need to determine how many times the two taxi drivers reach the same traffic light at the same time while following their given routes. We can count this by comparing the sequence of traffic lights each taxi visits and noting when they overlap. The Yellow taxi's route is: E-A-B-A-D-B-A-G-B-G-C-B. The Blue taxi's route is: H-C-B-A-C-B-C-G-F-B-C-B.

By examining the sequences, we can determine the overlaps:

• Both taxis are at traffic light B at the 3rd position in their routes.
• They both visit C as their 4th traffic light.
• Again, both are at B as their 6th traffic light.
• Both taxis reach B for the 9th time in their respective routes.
• Finally, they both reach C as the 11th traffic light.

In conclusion, the two taxis reach the same traffic light at the same time on five occasions.