Discussion
Four cities P, Q, R and S are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train.
If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?
Answer: A
The minimum time is 6 hours 30 minutes.
The routes are one-way: from R the only train goes to Q, from Q only to P, from P to R or S, and from S to Q or R. So the trip must go R, Q, P, S and back to R.
- Leave R at 7:00 (first train), reach Q at 8:00.
- Q's trains leave at 5:00, 7:00, 9:00 ..., so leave at 9:00 and reach P at 10:00.
- P's trains leave at 8:00, 9:30, 11:00 ..., so leave at 11:00 and reach S at 12:00.
- S's trains leave every 45 minutes from 8:00: ... 11:45, 12:30. Leave at 12:30 and reach R at 13:30.
From 7:00 to 13:30 is 6 hours 30 minutes. The shorter options count only the 4 hours of travel plus part of the waiting; every connection above is the first one available, so no faster trip exists.
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