Choosing the Bus to the Museum
The Class 7 committee at Mirpur Girls' High School is planning a museum visit for 44 people: 40 students and 4 teachers. The museum admits school groups only for the 10:30 a.m. slot and will not let a late group in.
Two buses are available: Bus Alo - 52 seats, Tk 3,200 for the whole bus, leaves school at 8:00, journey time 2 hours 30 minutes. Bus Bela - 40 seats, Tk 2,600 for the whole bus, leaves school at 7:40, journey time 2 hours 20 minutes; it cannot carry more than 40 passengers.
A seven-seat microbus can be hired as an extra vehicle for Tk 900; on the same road it needs 10 minutes more than Bus Bela.
School rule: no student may travel in a vehicle without a teacher, and every vehicle used must carry at least one teacher.
The head teacher says, 'Take the cheaper bus - ten minutes here or there does not matter.'
1. Work out the cost, seat use and arrival time of every plan that follows the school's teacher rule. Which plans reach the museum in time for the 10:30 slot?
Read the worked answer
Plan A - Bus Alo alone. 52 seats ≥ 44, so all 40 students and 4 teachers travel together and the rule is met four times over. Cost Tk 3,200. Arrival: 8:00 + 2 h 30 min = 10:30 exactly.
Plan B - Bus Bela plus microbus. Bela alone is impossible (40 seats < 44 people). Together: 40 + 7 = 47 seats ≥ 44. One workable split is Bela: 37 students + 3 teachers = 40 seats; microbus: 3 students + 1 teacher = 4 of its 7 seats. Cost Tk 2,600 + 900 = Tk 3,500. Arrival: Bela 7:40 + 2 h 20 min = 10:00; microbus 7:40 + 2 h 30 min = 10:10.
In time for the slot? Both plans technically arrive by 10:30, but Plan A arrives on the minute, with no time to park, walk in or count heads, while Plan B has 20 minutes to spare (30 for the larger group). Plan A is one delayed traffic light away from being refused.
2. Compare the cost per person and judge the head teacher's instruction.
Read the worked answer
Plan A: 3200 ÷ 44 = about Tk 72.7 per person. Plan B: 3500 ÷ 44 = about Tk 79.5 per person. The difference is Tk 300 in total, roughly Tk 6.8 per person - about the price of a packet of biscuits.
The head teacher is right about the money and wrong about the risk. The real gap is not 'ten minutes': Plan A arrives at 10:30 exactly, so its margin is zero. A late start, a traffic hold-up or five minutes lost loading the bus means the group misses the only slot - and the whole Tk 3,200, plus the children's day, is wasted. Plan B buys 20–30 minutes of safety margin for Tk 300.
Recommendation: Plan B. Spending 9% more to protect the entire trip is the better judgement; the cheapest option is not the cheapest if it can fail completely.
3. Two more students join at the last moment, making 46 people. Re-check the numbers. What would you confirm with the museum before booking, and why does it matter here?
Read the worked answer
Re-check with 46 people (42 students, 4 teachers).
- Plan A: 52 seats ≥ 46 → still fits, still Tk 3,200, still arrives 10:30 with no margin.
- Plan B: 47 seats ≥ 46 → still fits, but only just. One split: Bela 36 students + 3 teachers = 39 seats; microbus 6 students + 1 teacher = 7 seats (full). Spare capacity falls from 3 seats to 1.
So the answer does not change - Plan B is still the safer choice - but the margin has almost gone: one more pupil would break Plan B while Plan A would still absorb the extra. Plan B is now also less comfortable.
What to confirm with the museum: whether the 10:30 slot means entry strictly at 10:30, or whether a group arriving up to, say, 10:45 is still admitted. This single fact decides the question: if there is a grace period of 15–20 minutes, Plan A's zero margin is no longer dangerous and the cheaper bus becomes the sensible choice. Also worth confirming that the microbus can drop its passengers at the gate and park. Never assume a timetable slack that has not been checked.