A professor holds office hours during final exam week and discovers much to his dismay that his sudden popularity affords him little time to engage in his favorite activity, watching cat videos.Fifteen students per hour arrive at his office and he patiently answers questions, averaging three minutes per student.A student joins the line at 9:45 am and the test is at 10:00 am the same morning.How much time does the student have after getting his question answered to get to the exam room?
A)12 minutes
B)9 minutes
C)6 minutes
D)3 minutes

Question

Quizplus · Accepted Answer

Given that the professor averages three minutes per student and fifteen students arrive per hour, this means he can see five students per hour (60 minutes / 3 minutes per student). If a student joins the line at 9:45 am, they are effectively in line for the 10:00 am slot. Since the student is in line 15 minutes before the hour, they are the fifth person in line for that hour (as one student is seen every 12 minutes to make up five students an hour). Therefore, it will take 15 minutes (3 minutes per student times 5 students) from 9:45 am for the student to get their question answered, putting the time at 10:00 am exactly when the test starts. Thus, the student has no time left after getting their question answered to get to the exam room, making the correct answer 0 minutes, which is not an option provided. However, based on the options given and the scenario, there seems to be a misunderstanding in the calculation. Let's correct the approach:If the professor sees five students per hour (60/12 = 5), and a student arrives at 9:45 am, they are not the fifth in line based on the hourly capacity but rather based on the immediate queue. The correct calculation should consider the immediate wait time for the student arriving at 9:45 am, given the professor's rate of seeing students.The professor sees 15 students per hour, which means he sees one student every 4 minutes (60 minutes / 15 students). If a student joins the line at 9:45 am and each student takes 3 minutes, the student will be seen immediately as there's no indication of a queue before them. Therefore, they would spend 3 minutes getting their question answered.This means the student would have their question answered by 9:48 am, giving them 12 minutes to get to the exam by 10:00 am. The correct answer, based on the initial setup, should be A) 12 minutes, acknowledging an error in the initial explanation.

A Professor Holds Office Hours During Final Exam Week and Discovers