I have a lesson to do every day. If I do not complete it that very day, it turns overdue. I cannot complete any other lessons after that overdue lesson until I complete the overdue. I have eight overdue lessons already, plus the lesson for each day, and I complete two overdue lessons each day to catch up, but one new overdue lesson is added to my already overdues. Will I eventually catch up, and if so, how long would it take to catch up?

Answer 1

Let's break down your situation:

1. You have 8 overdue lessons.
2. You have a new lesson for each day, which adds 1 new overdue lesson daily.
3. Each day, you can complete 2 overdue lessons.

This means that essentially every day, you are dealing with the following:

• You complete 2 lessons from your total overdue pool.
• You also accrue 1 new overdue lesson.

So, each day, your overdue lessons decrease by 1 (because you complete 2 but add 1).

Calculation:

• You start with 8 overdue lessons.
• Each day, the net change in your overdue lessons is:
  • 8 (starting) - 2 (completed) + 1 (new) = 7 lessons after 1 day.
• After 2 days:
  • 7 (previous) - 2 (completed) + 1 (new) = 6 overdue lessons.
• After 3 days:
  • 6 (previous) - 2 (completed) + 1 (new) = 5 overdue lessons.
• After 4 days:
  • 5 (previous) - 2 (completed) + 1 (new) = 4 overdue lessons.
• After 5 days:
  • 4 (previous) - 2 (completed) + 1 (new) = 3 overdue lessons.
• After 6 days:
  • 3 (previous) - 2 (completed) + 1 (new) = 2 overdue lessons.
• After 7 days:
  • 2 (previous) - 2 (completed) + 1 (new) = 1 overdue lesson.
• After 8 days:
  • 1 (previous) - 2 (completed) + 1 (new) = 0 overdue lessons.

After 8 days, you will have caught up with your overdue lessons.

From this point forward, since you will have cleared all your overdue lessons, you can focus on completing the new daily lessons.

Thus, it will take you 8 days to catch up on your overdue lessons. After that, you will no longer have any overdue assignments as long as you continue completing your daily lesson.