Reading a Bus Timetable Under Pressure
Mia catches a bus to a regional sports carnival. The timetable shows buses leaving her stop at 7:15 am, 7:45 am, 8:20 am and 9:05 am. The trip takes 50 minutes on weekdays but 65 minutes on Saturdays because of roadworks. The carnival starts at 9:30 am and students must arrive 20 minutes early for roll call. Mia needs to walk 8 minutes from the bus stop to the venue. Today is Saturday. Mia's friend says, 'Just catch the 8:20 - you'll be fine.' Mia is not sure. She also has a backup plan to catch the 7:45 if she wakes up early enough.
1. Which bus should Mia catch to arrive on time for roll call? Show your working for each option.
Read the worked answer
Roll call is 20 minutes before 9:30 am = 9:10 am. Mia must be at the venue by 9:10 am. Add the 8-minute walk, so she must get off the bus by 9:02 am.
Saturday trip time is 65 minutes. Check each bus:
- 7:15 am + 65 min = 8:20 am arrival at stop; + 8 min walk = 8:28 am at venue. Early.
- 7:45 am + 65 min = 8:50 am; + 8 min = 8:58 am. On time.
- 8:20 am + 65 min = 9:25 am; + 8 min = 9:33 am. Late for the 9:10 roll call.
- 9:05 am is even later.
So the 8:20 bus is too late. The friend is wrong. Mia must catch the 7:45 am bus to arrive at 8:58 am, which is 12 minutes before roll call. The 7:15 bus also works but is unnecessarily early.
2. Mia's friend used the weekday trip time. Explain how using the wrong trip time changes the answer, and what this reveals about the friend's reasoning.
Read the worked answer
With the weekday time of 50 minutes:
- 8:20 am + 50 min = 9:10 am at the stop; + 8 min walk = 9:18 am at the venue.
Even with the shorter weekday time, 9:18 am is after the 9:10 am roll call. So the 8:20 bus fails under either trip time - the friend's conclusion is wrong regardless.
However, using 50 minutes for the 7:45 bus gives 8:35 am + 8 min = 8:43 am, which still works. The wrong trip time mainly changes how much spare time Mia thinks she has, not which bus is the latest possible one.
The deeper point: the friend reasoned from a rough memory ('about an hour') instead of checking the Saturday condition. The correct method is to fix the deadline (9:10 am), subtract the walk (9:02 am), then subtract the correct trip time (65 min) to find the latest departure (7:57 am). The 7:45 bus is the latest one before 7:57 am.
3. Suppose Mia misses the 7:45 bus. What is her best remaining option, and what should she tell the carnival organisers?
Read the worked answer
If she misses 7:45, the next bus is 8:20 am, arriving at the venue at 9:33 am - 23 minutes after roll call.
Her best remaining option is the 8:20 am bus, because it is the earliest still available. She cannot arrive on time by bus.
She should contact the organisers before 9:10 am to explain she will be about 23 minutes late and ask whether she can still be marked present or join a later event. A strong answer recognises that the practical judgement is not just 'which bus' but 'communicate early' - waiting until she arrives late makes the problem worse.
An alternative is to ask a parent for a lift, which could get her there before 9:10 am. The answer should weigh the options rather than assume the bus is the only choice.