Hubert is a hard-working college junior. One Sunday, he decides to work nonstop
ID: 1145203 • Letter: H
Question
Hubert is a hard-working college junior. One Sunday, he decides to work nonstop until he has answered 150 practice problems for his economics 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.
Use the table to answer the following questions.
The marginal, or additional, gain from Hubert’s second hour of work, from 9:00 AM to 10:00 AM, isproblems.
The marginal gain from Hubert’s fourth hour of work, from 11:00 AM to noon, isproblems.
Later, the teaching assistant in Hubert’s economics course gives him some advice. “Based on past experience,” the teaching assistant says, “working on 52.5 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?
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
Time Total Problems Answered 8:00 AM 0 9:00 AM 60 10:00 AM 105 11:00 AM 135 Noon 150Explanation / Answer
Marginal gain from Huberts second hour of work is the difference between the number of problems answered in the second hour and the first hour.
Marginal Gain = (105 - 60) = 45 problems.
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Again, Marginal gain from fourth hour is the difference between the number of problems solved in fourth hour(noon) and the third hour.
Marginal Gain = (150 - 135) = 15 problems.
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Marginal Gains:
1st hour : 60 - 0 = 60 problems
2nd hour : 105 - 60 = 45 problems
3rd hour : 135 - 105 = 20 problems
4th hour : 150 - 135 = 15 problems.
Now it is given that solving 52.5 problems or reading the textbook for 1 hour both raises the exam score by the same amount. Thus from the above calculated marginal gains it can be seen that his problem solving is highest for the 1st hour which is 60 which is in case higher than 52.5. But the marginal gains for the 2nd 3rd and 4th hours are less than that of 52.5. Which means that he can use this 3 hours for reading the textbook in order to get the best exam score instead of solving problems, since solving problems for the 2nd 3rd and 4th hours will not help him to get the best examscore as he is unable to solve more or equal to 52.5 problems for the 2nd 3rd and 4th hours.
So, Hubert should spent 1 hour working on problems and 3 hours reading.
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