Question
Darnell is a hard-working college sophomore. One Saturday, he decides to work nonstop until he has answered 200 practice problems for his math course. He
Darnell is a hard-working college sophomore. One Saturday, he decides to work nonstop until he has answered 200 practice problems for his math course. He starts work at 8:00 AM and uses a table to keep track of his progress throughout the day. He notices that as he gets tired, it takes him longer to solve each problem.
TimeTotal Problems Answered8:00 AM09:00 AM8010:00 AM14011:00 AM180Noon200Use the table to answer the following questions.
The marginal, or additional, gain from Darnell's second hour of work, from 9:00 AM to 10:00 AM, isproblems.
The marginal gain from Darnell's fourth hour of work, from 11:00 AM to noon, isproblems.
Later, the teaching assistant in Darnell's math course gives him some advice. "Based on past experience," the teaching assistant says, "working on 70 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 his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems, and how many should he have spent reading?
0 hours working on problems, 4 hours reading
1 hour working on problems, 3 hours reading
2 hours working on problems, 2 hours reading
4 hours working on problems, 0 hours reading
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