Question

Ana 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. Time Total Problems Answered 8:00 AM 0 9:00 AM 80 10:00 AM 140 11:00 AM 180 Noon 200 The marginal, or additional, gain from Ana’s second hour of work, from 9:00 AM to 10:00 AM, is ? problems. The marginal gain from Ana’s fourth hour of work, from 11:00 AM to noon, is ? problems. Later, the teaching assistant in Ana’s chemistry course gives her some advice. The teaching assistant says, “Based on past experience, 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 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? A. 0 hours working on problems, 4 hours reading B. 1 hour working on problems, 3 hours reading C. 3 hours working on problems, 1 hour reading D. 4 hours working on problems, 0 hours reading

Answer 1

60 ; 20

B.) 1 hour working on problems, 3 hours reading

Explanation:

Given the information :

Time - - - Total problems Answered

8am: - - - - 0

9am: - - - - 80

10am: - - - - 140

11am: - - - - -180

noon: - - - - 200

The marginal, or additional, gain from Ana’s second hour of work, from 9:00 AM to 10:00 AM, is ?

(Total problem answered at 10 a.m - Total problems Answered at 9a.m)

(140 - 80) = 60

The marginal gain from Ana’s fourth hour of work, from 11:00 AM to noon, is ?

(Total problem answered at Noon - Total problems Answered at 11a.m)

(200 - 180) = 20

In other to get the best possible exam score,

Since it is assumed that

Solving 70 problems is equivalent to 1 hour of reading in terms of score improvement

Also, it is assumed that the same number of pages is covered for every hour spent whine reading.

Hence it is only during the first hour, that is (8:00 - 9:00) that she was able to solve above 70 questions (80 - 0). Number of questions solved during subsequent hours were not up to 70, hence it would have been more rewarding if they had been used for reading.

Hence, she should have spent 1 hour working on problems and 3 hours reading