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 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 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. A) They do not reach any traffic lights at the same time. B) Two times C) Five times D) Six times

Answer 1

After comparing the routes of both taxis step by step, both taxis reach the same traffic light at the same time on two occasions, and the final answer is option B) Two times.

Step-by-step explanation:

To solve this question, we must compare the routes of both taxis and look for instances where they visit the same traffic light at the same step in their route. The Yellow Taxi takes the following route: E - A - B - A - D - B - A - G - B - G - C - B. The Blue Taxi takes the route: H - C - B - A - C - B - C - G - F - B - C - B.

Analyzing the pattern and step by step progression, the taxis reach the same traffic light simultaneously at the following points:

1. Both taxis reach 'B' at their third step.
2. Both taxis reach 'B' again at their seventh step.

Therefore, Yellow Taxi and Blue Taxi reach the same traffic light at the same time on two occasions. The final answer is option B) Two times.

Answer 2

By comparing the two taxi routes, it is evident that they arrive at the same traffic light at the same time on two occasions, at traffic lights A and B.

Step-by-step explanation:

The question involves analyzing the routes taken by two taxis to determine if and how often they reach the same traffic light at the same time. To find the answer, we have to track the sequence in which both taxis arrive at each traffic light and compare the sequences. After meticulously comparing the two sequences, we can conclude how many times the Yellow Taxi and Blue Taxi reach the same traffic light simultaneously.

The routes for the Yellow Taxi and Blue Taxi are as follows:

• 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

By comparing these routes step by step, it would appear they reach the same traffic lights at:

• A at the same time once (second stop for Yellow, fourth stop for Blue)
• B at the same time once (third stop for Yellow, third stop for Blue)

Hence, the Yellow Taxi and Blue Taxi arrive at the same traffic light at the same time on two occasions, which corresponds to option B.