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Maria is a hard-working college sophomore. One Sunday, she decides to work nonstop until she has answered 100 practice problems for her math 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 40
10:00 AM 70
11:00 AM 90
Noon 100

Use the table to answer the following questions.
The marginal, or additional, gain from Maria’s first hour of work, from 8:00 AM to 9:00 AM, is _______ problems.
The marginal gain from Maria’s third hour of work, from 10:00 AM to 11:00 AM, is _______ problems.
Later, the teaching assistant in Maria’s math course gives her some advice. "Based on past experience," the teaching assistant says, "working on 25 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) 2 hours working on problems, 2 hours reading
d) 3 hours working on problems, 1 hour reading

Respuesta :

proz

Answer:

The correct answers are:

i. The marginal, or additional, gain from Maria’s first hour of work, from 8:00 AM to 9:00 AM, is  40   problems.

ii. The marginal gain from Maria’s third hour of work, from 10:00 AM to 11:00 AM, is   20   problems

iii. 2 hours working on problems, 2 hours reading (c)

Explanation:

i. The marginal gain from 8:00 AM to 9:00 AM is calculated thus:

work done at 8:00 AM = 0 problems

Work done at 9:00 AM = 40 problems

Marginal gain = (Work done at 9:00 AM) - (work done at 8:00) = 40 - 0 = 40 problems

ii. work done at 10:00 AM = 70 problems

work done at 11:00 AM = 90 problems

Marginal gain = 90 - 70 = 20 problems

iii. To get the best exam score, the most number of problems possible in total must be answered within the 4-hour period, and this is determined as follows:

we are told that Maria gets tired as time progresses and the number of questions answered reduces we notice the following numbers of questions answered in each hour:

8:00 AM to 9:00 AM = 40 - 0 = 40 problems (hour 1)

9:00 AM to 10:00 AM = 70 - 40 = 30 problems (hour 2)

10:00 AM to 11:00 AM = 90 - 70 = 20 problems (hour 3)

11:00 AM to Noon = 100 - 90 = 10 problems (hour 4)

Also, we are told that;

1 hour of reading = 25 problems

Comparing the reading and solving problems, we see that the number of problems solved in hour-1 and hour-2  (40 and 30 respectively) are more than the equivalent number of problems solved in reading for 1 hour, while hour-3 and hour-4 (20 and 10 respectively), have lesser equivalent number of problems each, than reading for one hour. Therefore to make the most out of the 4 hours, Maria will spend the first 2 hours solving problems and the next two hours reading, giving a total of: 40 + 30 + 25 + 25 = 120 problems solved.

The marginal gain from Maria’s first hour of work is 40 problems.

The marginal gain from Maria’s third hour of work is 20 problems.

In order to get the best score possible, the hours that should be spent working on problems is 2 hours and the hours spent reading is 2 hours.

What is Marginal Gain?

Marginal gain is the change in total gain when total time worked increases by one unit. Marginal gain = change in total gain / change in total hours

  • Marginal gain when problems are answered for 1 hour = 40 - 0 = 40
  • Marginal gain when problems are answered for 2 hours = 70 - 40 = 30
  • Marginal gain when problems are answered for 3 hours =  90 - 70 = 20
  • Marginal gain when problems are answered for 4 hours = 100 - 90 = 10

What is the best use of Maria's time?

Due to the fact that solving 25 problems an hour is equivalent to 1 hour of reading. Maria should solve problems for 2 hours. This is because the marginal gain from solving problems for 2 hours is greater than 25. The other two hours should be spent reading.

To learn more about marginal gain, please check: https://brainly.com/question/13267735

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