Answer to February 2007 Problem

In the comic strip below, how many hours of homework will she have to do in 36 weeks?

 

Solution to the Problem:

She would do 68,719,476,735 seconds of homework or 19,088,743 hours!!!!
However, it would be physically impossible to fulfill the contract. The number of seconds in a week is given by 7 x 24 x 60 x 60 = 604,800 seconds.
On the 20th week, she would have to do 219 or 524,288 seconds of homework.
On the 21st week, she would have to do 220 or 1,048,576 seconds of homework, which is more than the number of seconds in a week!

So, the real answer would be 10,725,375 seconds or 178,756.25 minutes or 2,979 hours of homework.
For the first 20 weeks, she would do 1,048,575 seconds of homework. Then the best she could do after that would be 604,800 seconds per week for the remaining 16 weeks as long as she doesn't sleep or eat or go to school.

To see this pattern, try a table:
Week # Seconds of Homework that Week Total Seconds of Homework
1 1 = 20 1 = 21 - 1
2 2 = 21 3 = 22 - 1
3 4 = 22 7 = 23 - 1
4 8 = 23 15 = 24 - 1
... ... ...
20 524,288 = 219 1,048,575 = 220 - 1
21 1,048,576 = 220
Not possible!		 2,097,151 = 221 - 1
... ... ...
36 = 34,359,738,368 = 235 68,719,476,735 = 236 - 1

David and Judy Dixon were the first to note that she would not be able to keep up with her homework by the 21st week.

Correctly solved by:

1. James Alarie University of Michigan -- Flint
Flint, Michigan
2. Sagar Patel Brookstone School
Columbus, Georgia
3. David & Judy Dixon Bennettsville, South Carolina
4. Shaan Arora Brookstone School
Columbus, Georgia
5. Richard K. Johnson La Jolla, California
6. John Funk Ventura, California
7. Tristan Collins Virginia Tech
Blacksburg, Virginia
8. Mr. Robb's Discrete Math Class John Handley High School
Winchester, Virginia
9. Neal Amos Brookstone School
Columbus, Georgia