The Night-Shift Bus Schedule
A community college runs a free shuttle between its main campus and a distant parking lot. The printed schedule reads: "Shuttle departs the lot at 6:40 a.m., 7:20 a.m., 8:00 a.m., and every 40 minutes thereafter until 10:00 p.m." A student named Dara arrives at the lot at 7:05 a.m. She needs to be in a classroom building a 6-minute walk from the campus stop by 7:45 a.m. The ride itself takes 12 minutes. A sign taped to the shelter adds: "Last departure from campus back to the lot is 10:20 p.m." Dara reads the schedule quickly and worries she will be late.
1. Determine which departure Dara should catch and whether she will arrive on time. Show your reasoning step by step.
Read the worked answer
Find the departures. The listed times are 6:40, 7:20, 8:00. The pattern is "every 40 minutes thereafter," so adding 40 minutes to 7:20 gives 8:00 - consistent.
Match to Dara's arrival. Dara reaches the lot at 7:05. The 6:40 bus has already left. The next departure is 7:20.
Work forward from 7:20.
- Ride: 12 minutes → campus stop at 7:32.
- Walk: 6 minutes → building at 7:38.
Compare to deadline. 7:38 is before 7:45, so she arrives 7 minutes early. She should catch the 7:20 shuttle. Her worry is unfounded - but only because the next bus (8:00) would put her at the building at 8:18, which would be late. The margin is real, not imaginary.
2. The taped sign about the 10:20 p.m. return trip is not part of the printed 40-minute pattern. What does this tell a careful reader about how to treat the two sources of information?
Read the worked answer
The printed schedule and the taped sign are separate sources with separate scopes. The printed line governs outbound departures from the lot on a 40-minute cycle ending at 10:00 p.m. The sign governs only the final return trip.
A careful reader should not force the sign into the 40-minute pattern. If you extended the cycle past 10:00 p.m., you would predict 10:40 - but the sign says 10:20, which breaks the pattern. That is a signal that the sign is an exception or addition, not a continuation.
The practical rule: read each statement for what it explicitly covers (direction, time window), and do not assume one rule applies to a case it never mentions. A rider who assumed "every 40 minutes" applied to returns would miss the 10:20 bus entirely.