Question

Becky is a hard-working college sophomore. One Sunday, she decides to work nonstop until she has answered 200 practice problems for her physics 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

Use the table to answer the following questions.

The marginal, or additional, gain from Becky’s first hour of work, from 8:00 AM to 9:00 AM, isproblems.

The marginal gain from Becky’s third hour of work, from 10:00 AM to 11:00 AM, isproblems.

Later, the teaching assistant in Becky’s physics course gives her 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 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?

0 hours working on problems, 4 hours reading

1 hour working on problems, 3 hours reading

3 hours working on problems, 1 hour reading

4 hours working on problems, 0 hours reading

Answer 1

(i)

Marginal Gain = Change in Total Gain / Change in total Time

At 8 AM she started working and hence she solved 0 questions at 8 AM

We can see from above table that At 9 AM she solved 80 problems

So, Marginal Gain During First hour (between 8 AM and 9 AM) = (80 - 0)/1 (Note Change in Time = 1 hour)

= 80

Hence, The marginal, or additional, gain from Becky’s first hour of work, from 8:00 AM to 9:00 AM, is 80 problems

(ii)

Marginal Gain = Change in Total Gain / Change in total Time

We can see from above table that At 10 AM she solved 140 problems

We can see from above table that At 11 AM she solved 180 problems

So, Marginal Gain During Third hour (between 10 AM and 11 AM) = (180 - 140)/1 (Note Change in Time = 1 hour)

= 40

Hence, The marginal, or additional, gain from Becky’s Third hour of work, from 10:00 AM to 11:00 AM, is 40 problems

(iii)

The correct answer is (b) 1 hour working on problems, 3 hours reading

Now, She has the new information that working on 70 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.

With this information She will prefer reading Book If during that Hour she was able to solve less than 70 Problems or we can say that She will prefer reading Book If Marginal Gain of that hour < 70

Marginal Gain of first hour when she solved problems as calculated above is 80 > 70. Hence At the first hour she will prefer to solve problems.

Marginal Gain of second hours is given by:

We can see from above table that At 9 AM she solved 80 problems

We can see from above table that At 11 AM she solved 140 problems

So, Marginal Gain During second hour (between 9 AM and 10 AM) = (140 - 80)/1 (Note Change in Time = 1 hour)

= 60

Marginal Gain of second hour when she solved problems as calculated above is 60 < 70. Hence She wil,l prefer to read book during second hour.

Note that Marginal Gain is decreasing when she solved problems but When she read books her marginal gain = 70 problems.

So From second hour on wards she will read books

So, she will work on problems for 1 hour and read textbook for 3 hours

Hence, the correct answer is (b) 1 hour working on problems, 3 hours reading