Kyoko is a hard-working college junior. one saturday, she decides to work nonstop until she has answered 200 practice problems for her chemistry 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.
8: 00am - 0
9: 00am - 80
10: 00am - 140
11: 00am - 180
12: 00am - 200
the marginal, or additional, gain from kyoko's first hour of work, from 8: 00 am to 9: 00 am, is 80 problems.
the marginal gain from kyoko's third hour of work, from 10: 00 am to 11: 00 am, is 40 problems.
later, the teaching assistant in kyoko's chemistry course gives her some advice. "based on past experience," the teaching assistant says, "working on 30 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?