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?

2 hours working on problems, 2 hours reading

Step-by-step explanation:

The question is incomplete. Here is the complete question:

Ben is a hard-working college senior. One Thursday, he decides to work nonstop until he has answered 150 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.

Time          |   Total Problems Answered

8:00 AM   |   0

9:00 AM   |   60

10:00 AM |   105

11:00 AM  |   135

Noon   |   150

The marginal, or additional, gain from Ben's first hour of work, from 8:00 AM to 9:00 AM, is 60 problems.

The marginal gain from Ben's third hour of work, from 10:00 AM to 11:00 AM, is 30 problems.

Later, the teaching assistant in Ben's math course gives him some advice. Based on past experience, the teaching assistant says, "working on 40 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?

The marginal or additional gain in the above question is calculated by obtaining the difference in problems solved between two selected time frames . For example, the marginal or additional gain from Ben's 11 AM to Noon work is :

Additional gain from 11 AM to Noon = 150 - 135 = 15 problems

Ben should therefore make his decision at the margin. Each hour, he should select the option that will improve his exam grade by the largest amount. If he can do more than 40 problems in an hour, working on problems will help raise his grade more for that hour than reading would.The marginal gain from the first hour is 60 problems. The marginal gain from the second hour is 45 problems. He will stop there, because he will get only 30 problems done if he spends the third hour working on problems. Therefore, he should stop working on problems and spend his remaining 2 hours reading instead.

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