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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.

1. The marginal, or additional, benefit from Andrew’s second hour of work, from 9:00 AM to 10:00 AM, is ___ problems.

2. The marginal benefit from Andrew’s fourth hour of work, from 11:00 AM to noon, is ___ problems.

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 :

Final answer:

Andrew's marginal benefit for the second and fourth hours of work is 30 and 10 problems, respectively. To maximize exam scores, given the teaching assistant's advice, Andrew should likely split his 4 hours of study time equally between solving practice problems and reading, making option c (2 hours each) the most beneficial.

Explanation:

Andrew's marginal benefit during his second hour of work, from 9:00 AM to 10:00 AM, is the additional number of problems he completed in that hour compared to the previous hour. He solved 70 problems by 10:00 AM and had already solved 40 problems by 9:00 AM, so the marginal benefit is 70 - 40 = 30 problems.

The marginal benefit from Andrew's fourth hour of work, from 11:00 AM to noon, is the additional number of problems he completed in that hour. By noon, he had solved 100 problems, and by 11:00 AM he had solved 90, so the marginal benefit is 100 - 90 = 10 problems.

Considering the teaching assistant's advice, Andrew should aim to work on a number of problems that raises his score as much as possible during his 4 hours of study time. If each set of 62.5 problems solved is equivalent to one hour of textbook reading in terms of exam score benefit, then in four hours, he should allocate his time such that he solves close to multiples of 62.5 problems, while also making sure to spend some time on reading. We can see from the earlier table that in the first hour he solves 40 problems, and in two hours, he solves 70 problems. Therefore, since 62.5 problems have the same benefit as one hour of reading, it is better to study problems for at least two hours (to solve more than 62.5 problems) and spend the remaining time on reading. Solving for the exact number of hours can be tricky based solely on the information provided, but knowing that Andrew can solve more problems in earlier hours, he should probably split his time equally between problem-solving and reading to maximize the benefit. This makes option c (2 hours working on problems, 2 hours reading) the most likely answer.

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Rewritten by : Barada

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.