Kyoko is a hard-working college senior. One Saturday, she decides to work nonstop until she has answered 150 practice problems for her math course. She starts work at 8:00 AM and uses a table to keep track of her progress throughout the day. She notices that as she gets tired, it takes her longer to solve each problem.
Time
Total Problems Answered
8:00 AM 0
9:00 AM 60
10:00 AM 105
11:00 AM 135
Noon 150
Use the table to answer the following questions.
The marginal, or additional, benefit from Kyoko’s second hour of work, from 9:00 AM to 10:00 AM, is
45
problems.
The marginal benefit from Kyoko’s fourth hour of work, from 11:00 AM to noon, is
15
problems.
Later, the teaching assistant in Kyoko’s math course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 52.5 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.” For simplicity, assume students always cover the same number of pages during each hour they spend reading.
Given this information, in order to use her 4 hours of study time to get the best exam score possible, how many hours should she have spent working on problems, and how many should she have spent reading?
1 hour working on problems, 3 hours reading
2 hours working on problems, 2 hours reading
3 hours working on problems, 1 hour reading
4 hours working on problems, 0 hours reading