Problem 7-12 (Algo)

How much time, on average, would a server need to spend on a customer to achieve a service rate of 120 customers per hour?

Note: Round your answer to 2 decimal places.

Question

Problem 7-12 (Algo)

How much time, on average, would a server need to spend on a customer to achieve a service rate of 120 customers per hour?

Note: Round your answer to 2 decimal places.

BlackTom AI · Accepted Answer

Service rate μ (customers per hour) is the reciprocal of the average service time t (hours per customer): t = 1/μ.

1) Relevant concepts
- Service rate μ (customers/hour) = number of customers a server can serve in one hour.
- Average service time t (hours/customer) = 1/μ.
- Unit conversion: 1 hour = 60 minutes.

2) Step-by-step reasoning
- Given μ = 120 customers/hour.
- Compute average service time in hours: t_hours = 1 / 120.

3) Calculations (all intermediate steps)
- t_hours = 1 / 120 = 0.008333333... hours per customer.
- Convert to minutes: t_minutes = t_hours × 60 = 0.008333333... × 60.
- t_minutes = 0.5 minutes.

4) Why this is correct
- The service rate of 120 customers per hour means each customer, on average, takes the fraction of an hour equal to the reciprocal of 120. Converting that fraction of an hour to minutes yields 0.5 minutes (30 seconds), so each customer is served in half a minute on average.

5) Why other answers would be incorrect
- Entering 0.00833 as the answer would be hours, not minutes (the prompt asks for minutes).
- Answering 0.50 hours would be 30 minutes per customer, which contradicts a 120 customers/hour rate.
- Any answer that does not apply the reciprocal relation or that forgets to convert hours → minutes is incorrect.

Conclusion: The average service time required is 0.50 minutes, which matches the provided correct answer (0.50).

Problem 7-12 (Algo) How much time, on average, would a server need to spend on a customer to achieve a service rate of 120 customers per hour? Note: Round your answer to 2 decimal places.未知题型

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