One Tap, 109 Students, 40 Minutes
The school has one working tap near the toilet block. On normal days, 109 students must wash their hands with soap before lunch: Grade 3 has 30, Grade 4 has 32, Grade 5 has 35, and the Special Unit has 12. The lunch break is 40 minutes. One student at the tap takes about 20 seconds, but the 12 students in the Special Unit need about 40 seconds each because an adult helps them. Only one teacher can supervise the tap. There is soap and running water, but no second tap. The principal wants a rota that is fair, finishes within the break, and does not let younger children miss playtime every day. A parent suggests hand sanitiser as a quick fix, but the children's hands are often muddy after play.
1. Calculate the minimum time needed for all 109 students to wash if they use one tap. Is 40 minutes enough? Show your working.
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Step 1 – Students who need 20 seconds:
109 − 12 = 97 students.
Step 2 – Time for those 97 students:
97 × 20 seconds = 1,940 seconds.
Step 3 – Time for the Special Unit:
12 × 40 seconds = 480 seconds.
Step 4 – Total time:
1,940 + 480 = 2,420 seconds.
2,420 ÷ 60 = 40 minutes 20 seconds.
Conclusion: The minimum washing time alone is 40 minutes 20 seconds, which is already 20 seconds longer than the 40-minute break. In real life there will also be a few seconds for each group to move to the tap and for the teacher to organise them. So one tap is not enough for a comfortable, fair handwashing rota in 40 minutes. The school needs a small change, such as starting one minute early or adding a second temporary tap.
2. Propose a fair rota for the 40-minute break. Include who goes first, how long each group gets, and what to do about the Special Unit.
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Fair rota:
- Special Unit first - 8 minutes. They need adult help and 40 seconds each, and they should not be rushed at the end of the break.
- Grade 3 - 10 minutes. The youngest ordinary class goes next so they still get playtime.
- Grade 4 - 10 minutes 40 seconds.
- Grade 5 - 11 minutes 40 seconds. The oldest class can wait longest and can help keep the queue orderly.
Total: 8 min + 10 min + 10 min 40 s + 11 min 40 s = 40 min 20 s.
Problem: This is 20 seconds over the break. The rota must be honest about that. The simplest fair fix is to start the Special Unit 1 minute before the bell, with the supervising teacher present. That gives 41 minutes and leaves about 40 seconds for movement between groups.
Rules: One teacher stands at the tap, one group queues at a time, and no one runs. If a class finishes early, the next group starts early rather than waiting. The Special Unit's adult helper stays with them for the whole 8 minutes.
3. A parent says hand sanitiser can replace handwashing. Do you agree? Give one reason for and one against, and state your final advice.
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I do not agree that sanitiser can fully replace handwashing here.
Reason for sanitiser: It is fast and can kill many germs on hands that look clean. It could help if the tap queue is long or if there is no soap for a short time.
Reason against sanitiser: The children's hands are often muddy after play. Sanitiser does not remove mud, soil or visible dirt, and it works poorly when hands are dirty. Soap and running water are needed to wash dirt away before eating.
Final advice: Keep soap and water as the main method before lunch. Use sanitiser only as a backup after hands are free of visible mud, or for a child who cannot wait for the tap. The school should also ask for a second tap or a temporary bucket tap with a small opening, because the calculation shows one tap cannot serve 109 students comfortably in 40 minutes.