A, B, C, D, E, and F are the six police stations in an area, which are connected by streets as shown below. Four teams - Team 1, Team 2, Team 3 and Team 4 patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
Which team patrols the street connecting Stations D and E at 10:15 hrs?
Correct Answer :
Team 3
Solution :
To determine which team patrols the street connecting Stations D and E at 10:15 hrs, let us analyze the constraints and reconstruct the paths taken by the teams step-by-step.
First, we establish the timeline and the travel rules:
- The patrolling starts at 09:00 hrs and ends at 12:00 hrs.
- The time taken to traverse any street connecting two police stations is 30 minutes. Therefore, the teams arrive at police stations at 30-minute intervals: 09:00, 09:30, 10:00, 10:30, 11:00, 11:30, and 12:00.
- At 10:15 hrs (which is exactly halfway between 10:00 hrs and 10:30 hrs), any team patrolling a street must be in transit between the station it was at at 10:00 hrs and the station it reaches at 10:30 hrs.
Let us look at the facts related to the positions of the teams at 10:00 hrs and 10:30 hrs:
1. Fact 2: Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
This means at 10:00 hrs:
- Team 2 is at Station E.
- Team 3 is at Station D.
2. Fact 3: Teams 1 and 3 are the only ones in station E at 10:30 hrs.
This means at 10:30 hrs:
- Team 3 is at Station E.
Since Team 3 is at Station D at 10:00 hrs and is at Station E at 10:30 hrs, it must travel directly from Station D to Station E during this 30-minute interval.
Therefore, at the midpoint of this journey, which is 10:15 hrs, Team 3 is patrolling the street connecting Stations D and E.
Thus, the correct answer is Team 3.
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