The Two-Train Problem: Planning a Museum Visit from a List of Facts
Your class is planning a one-day English activity at a museum in Sendai. The teacher gives you a list of facts, not a timetable you can copy. (1) The museum opens at 9:30 and closes at 17:00; last entry is 16:30. It is closed on Mondays. (2) The visit is on Tuesday, 14 November. (3) The group leaves school at 8:40 by bus; the bus takes 50 minutes to the bus stop, and the museum is a 10-minute walk from that stop. (4) The English tour lasts 70 minutes and starts only at 10:30 and 13:30. (5) Lunch is 40 minutes and must be between 12:00 and 13:00. (6) The return bus leaves the stop at 15:20; the next one is 16:05.
Two students say the 13:30 tour is safe. One says it is impossible. The teacher asks you to write the answer the class should trust, and to list what you still need to know before the plan is final.
1. Build the timeline for the 13:30 tour and decide whether the group can catch the 15:20 bus. Give actual clock times, not just yes or no.
Read the worked answer
Timeline (Tuesday, 14 November)
- 08:40 leave school
- 09:30 arrive at the bus stop (50 min)
- 09:40 arrive at the museum entrance (10-min walk)
- 10:30–11:40 first tour - also possible, because the group is already there
- 12:00–12:40 lunch (inside the required 12:00–13:00 window)
- 13:30–14:40 second tour
- 14:50 back at the bus stop
- 15:20 bus - 30 minutes of slack
Answer: yes, the 13:30 tour works. Each leg is added in order; the error students make is to stop at 14:40 and forget the walk back.
The 30-minute margin is enough for a slow exit and a toilet stop, not enough for shopping. Note also that 15:20 is not the last bus: 16:05 is a second chance, so the bus is not the real risk. The real risk is the school's return deadline, which is not among the facts.
2. A classmate writes in the final plan, 'We arrive at the museum at 9:30.' Is that right? Give the time the group actually reaches the entrance and name the mistake.
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Not right. 08:40 + 50 min = 09:30 is the bus stop, not the museum. The 10-minute walk puts the group at the entrance at 09:40.
The mistake is dropping one leg of the journey - the sentence is true of an earlier point in the same trip, which is exactly why it is dangerous: it looks checked. It matters twice. First, the plan claims the group is inside the building ten minutes before it is. Second, 09:30 is the opening time, so a reader may add a wrong idea ('we must wait outside'), when in fact the group arrives ten minutes after opening.
Safe version: 'We arrive at the bus stop at 9:30 and at the museum at 9:40.' Longer, but it cannot be misread.
3. List three things you still need to know before the plan is final, and say for each one what it could change.
Read the worked answer
Any three of these, each with a consequence:
- How many students are going. Bus capacity and tour group size are fixed. If the number is over the limit, the 13:30 tour may have to be split in two, and the second half cannot finish before the 15:20 bus.
- Whether 15:20 and 16:05 run on that Tuesday (school-day, Saturday, or holiday timetable). The fallback bus is the only thing protecting the plan, so an untested fallback is not a plan.
- The school's return deadline. If students must be back by 16:30, the 16:05 bus is useless and the 30-minute slack at the museum has to be protected instead.
- Whether the English tour must be booked in advance and whether bookings close on the day. A perfect timeline with no reservation is not a plan.
- Lunch arrangements. If the museum cafeteria closes at 12:30 or needs a group booking, the 12:00–12:40 slot is not automatic.
Rule of thumb: a fact is 'still needed' only if you can say what it would change. 'The entrance fee' is a real question but does not change the schedule.