A wise professor crafts a midterm that is beautiful to behold, painful to take, and a chore to grade
The first exam takes almost an hour and a half to grade (89 minutes and 24.7 seconds to be precise) but the second one takes only seventy-six minutes to complete. Realizing that learning effects are at work, the professor looks at his social calendar and spots an important social engagement at this time on the following day, exactly 24 hours from now. How long will it take to grade the third exam? How long will it take to finish grading exams for the entire class of 30 students?
What will be an ideal response?
Answer:
The second exam takes 76/89.41167 or 85% of the first, so the learning percentage is 85%.
The third exam will take
Tn = T1nb = 89.411 × 3ln(.85)/ln(2)
T3 = 89.411 × 3-0.2345
= 89.411 × 0.77298
= 69.10497 minutes
All 30 exams will take:
T1-n = T1
= 89.4118 minutes × 17.091
= 1528.137 minutes
= 25 hours 28 minutes 8.22 seconds
Our story does have a happy ending. Since he has already graded two exams in 89.4117 minutes and 76 minutes, only 1362.723 more minutes (22 hours 42 minutes and 43.38 seconds) are needed to grade the last 28 exams, giving him adequate time to grade papers and clean up before the big event.
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