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 the 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?

• A. 6 hours 30 minutes
• B. 3 hours 45 minutes
• C. 4 hours 30 minutes
• D. 5 hours 15 minutes

Hint:

To solve such travel problems, carefully consider the train schedules and the waiting time for each connecting train.

Answer 1

The Correct Option is A

Let's break down the journey step-by-step: Step 1: From R to S.
- The person starts at 7 AM from city R.
- Trains from R to S start at 7 AM and run every 60 minutes.
- Since the person starts at 7 AM, they can catch the first train to S at 7 AM itself.
- The travel time from R to S is 1 hour, so the person reaches S at 8 AM.
Step 2: From S to Q.
- At city S, the first train to Q departs at 8 AM with a frequency of 45 minutes.
- The person arrives at 8 AM, so they can catch the 8 AM train to Q.
- The travel time from S to Q is 1 hour, so the person reaches Q at 9 AM.
Step 3: From Q to P.
- At city Q, the first train to P departs at 5 AM with a frequency of 120 minutes.
- Since the person arrives at 9 AM, they will have to wait for the 10 AM train.
- The travel time from Q to P is 1 hour, so the person reaches P at 11 AM.
Step 4: From P to R.
- At city P, the first train to R departs at 8 AM with a frequency of 90 minutes.
- Since the person arrives at 11 AM, they will have to wait for the 11:30 AM train.
- The travel time from P to R is 1 hour, so the person reaches R at 12:30 PM.
Step 5: Total Time Calculation.
- The person starts the journey at 7 AM and returns to R at 12:30 PM.
- The total time taken is from 7 AM to 12:30 PM, which is 6 hours and 30 minutes.
Final Answer:
The minimum time required is 6 hours and 30 minutes.