Question

Andrew is a hard-working college senior. One Saturday, he decides to work nonstop until he has answered 100 practice problems for his physics 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.
Time Total Problems Answered
8:00 AM 0
9:00 AM 40
10:00 AM 70
11:00 AM 90
Noon 100

Use the table to answer the following questions.
The marginal, or additional, benefit from Andrew’s second hour of work, from 9:00 AM to 10:00 AM, isproblems.
The marginal benefit from Andrew’s fourth hour of work, from 11:00 AM to noon, isproblems.
Later, the teaching assistant in Andrew’s chemistry course gives him some advice. "Based on past experience," the teaching assistant says, "working on 62.5 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 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?

a) 0 hours working on problems, 4 hours reading
b) 1 hour working on problems, 3 hours reading
c) 2 hours working on problems, 2 hours reading
d) 3 hours working on problems, 1 hour reading

Answer 1

Solution:

By 9:00 AM, Andrew has answered 40 problems.

By 10:00 AM, Andrew has answered 70 problems.

So the marginal, or additional, gain from his work between 9:00 AM and 10:00 AM is

70−40=30 problems.

By 11:00 AM, Andrew has answered 90 problems.

By noon, Andrew has answered 100 problems.

So the marginal gain from the fourth hour, 11:00 AM to noon, is

100−90= 10 problems.