7. Solution. Suppose for clarity of reasoning that when a bite occurs, the Absent-Minded Scholar immediately pulls out and re-casts the fishing rod, and does so instantly. After this, he waits again. Consider a 6-minute time interval. During this time, on average, there are 3 bites on the first fishing rod and 2 bites on the second fishing rod. Therefore, in total, there are on average 5 bites on both fishing rods in these 6 minutes. Consequently, the average waiting time for the first bite is $6: 5=1.2$ minutes.
Answer: 1 minute 12 seconds.

Evaluation Criteria

| Correct and justified solution | 3 points |
| :--- | :---: |
| It is shown that on average there are 5 bites in 6 minutes, or an equivalent statement is proven | 1 point |
| The solution is incorrect or missing (in particular, only the answer is given) | 0 points |