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. Will I eventually catch up, and if so, how long would it take to catch up?

Answer 1

To determine if you will catch up and how long it will take, let's break down the situation:

1. Current Status:

   • You have 8 overdue lessons.
   • You have 1 lesson to complete each day.
   • You can complete 2 overdue lessons each day.

2. Daily Actions:

   • Each day, you complete 1 new lesson (the lesson for that day).
   • Additionally, you complete 2 overdue lessons.

3. Daily Progress:

   • Each day, you effectively manage to reduce the total number of lessons you need to complete by 3:
     • 1 lesson for that day (new lesson)
     • 2 overdue lessons

4. Calculation of Days to Catch Up:

   • You currently have a total of 8 overdue lessons.
   • Each day, you reduce the overdue count by 2 lessons.

On Day 1:

• You complete 1 new lesson and 2 overdue lessons.
• Overdue lessons remaining: 8 - 2 = 6

On Day 2:

• You complete 1 new lesson and 2 overdue lessons.
• Overdue lessons remaining: 6 - 2 = 4

On Day 3:

• You complete 1 new lesson and 2 overdue lessons.
• Overdue lessons remaining: 4 - 2 = 2

On Day 4:

• You complete 1 new lesson and 2 overdue lessons.
• Overdue lessons remaining: 2 - 2 = 0

At this point, you have caught up with your overdue lessons.

Now, let's summarize the daily progress:

• You had 8 overdue lessons.
• Each day you catch up by 2 lessons and also complete 1 lesson for that day.

It takes you 4 days to reduce the 8 overdue lessons to 0, while during those 4 days you have also completed 4 new lessons (1 each day).

Thus, after 4 days you will have:

• Overdue lessons: 0
• Completed lessons for today: 1 lesson/day × 4 days = 4 new lessons.

So, to summarize, you will catch up in 4 days, and after that, you will continue with your daily lessons as usual.