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 <u> 40 </u> problems.
ii. The marginal gain from Maria’s third hour of work, from 10:00 AM to 11:00 AM, is <u> 20 </u> 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.
