Kate is a hard-working college senior. One Thursday, she decides to work nonstop
ID: 1150422 • Letter: K
Question
Kate is a hard-working college senior. One Thursday, she decides to work nonstop until she has answered 250 practice problems for her economics 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.
Use the table to answer the following questions.
1. **The marginal, or additional, gain from Kate’s first hour of work, from 8:00 AM to 9:00 AM, is (???) problems.
2. **The marginal gain from Kate’s third hour of work, from 10:00 AM to 11:00 AM, is (???) problems.
Later, the teaching assistant in Kate’s economics course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 37.5 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.
3. 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
Time 8:00 AM 9:00 AM 10:00 AM 11:00 AM Noon Total Problems Answered 100 175 225 250Explanation / Answer
Following table shows the additional problems solved with each hour of study -
It can be seen that as Kate studies from 8 AM to 9 AM, she is able to solve 100 additional problems.
So,
The marginal, or additional, gain from Kate's first hour of work from 8 AM to 9AM is 100 problems.
It can be seen that as Kate studies from 10 AM to 11 AM, she is able to solve 50 additional problems.
So,
The marginal gain from Kate's third hour of work, from 10 AM to 11 AM is 50 problems.
Until Kate is able to solve 37.5 problems or more, she will devote each sucessive hour to solving problem. If she is able to solve less than 37.5 problems then she will devote each sucessive hour to reading textbooks.
The table shows that solving problems upto 11 AM enable Kate to solve more than 37.5 problems in each hour.
So, Kate will devote 3 hours on problems and 1 hour on reading.
Hence, the correct answer is the option (C).
Time Total problems solved Marginal or additional gain 8 AM 0 - 9 AM 100 (100 - 0) 100 10 AM 175 (175 - 100) 75 11 AM 225 (225 - 175) 50 Noon 250 (250 - 225) 25Related Questions
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