Question 14
A shop has four service counters numbered 1, 2, 3 and 4. Initially only counter 1 is open.
Each counter can hold at most 4 people, including the person being served if any. Service takes 2 minutes per person. If a customer arrives when the counters already have 4 people each, the next counter opens. However, a new counter needs 1 minute of preparation, so its first customer takes 3 minutes in total to finish; later customers take only 2 minutes.
A customer entering the shop checks counters 1–2–3–4 to find the first one with room and joins its queue. A customer arriving at exactly the time the front customer finishes service can still join that queue.
Initially two customers enter, and every minute two more enter, until there are 12 customers in total. After how many minutes will all 12 have been served?
Each counter can hold at most 4 people, including the person being served if any. Service takes 2 minutes per person. If a customer arrives when the counters already have 4 people each, the next counter opens. However, a new counter needs 1 minute of preparation, so its first customer takes 3 minutes in total to finish; later customers take only 2 minutes.
A customer entering the shop checks counters 1–2–3–4 to find the first one with room and joins its queue. A customer arriving at exactly the time the front customer finishes service can still join that queue.
Initially two customers enter, and every minute two more enter, until there are 12 customers in total. After how many minutes will all 12 have been served?