Question
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 ?
Options :
6 hours 30 minutes
3 hours 45 minutes
4 hours 30 minutes
5 hours 15 minutes
Answer :
6 hours 30 minutes
Solution :
The person starts from R at 7 AM and visits S and then return to R, if the follows the routes R → Q → P → S → R.
The person starts from R at 7 AM and reaches Q at 8 AM. At Q, if a person starts at 5 AM, then after each 120 mins, the next train will start. 5 AM → 7 AM → 9 AM.
The person starts from Q at 9 AM and reaches P at 10 AM. At P, if a person starts at 8 AM, then after each 90 mins, the next train will start. 8 AM → 9.30 PM → 11 AM.
The person starts from P at 11 AM and reaches S at 12 PM. At S, if a person starts at 8 AM, then after each 45 mins, the next train will start. 8 AM → 8.45 AM → 9.30 AM → 10.15 AM → 11 AM → 11.45 AM → 12.30 PM. The person starts from S at 12.30 PM and reaches R at 1.30 PM.
∴ the total time taken is (1.30 PM - 7 AM) = 6 hours 30 minutes.
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