Question

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?

Answer 1

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= 89.4116 × 3ln(.85)/3ln(.85)/ln(2)

T3= 89.4116 × 3-0.2345

= 89.4116× 0.77298

= 69.10497 minutes

All 30 exams will take:

= 89.4118minutes × 17.091

= 1528.137 minutes

= 25 hours28 minutes8.22seconds