7. Solution. For clarity, let's assume that when a bite occurs, the Absent-Minded Scholar immediately reels in and casts the fishing rod again, and does so instantly. After this, he waits again. Consider a 5-minute time interval. During this time, on average, there are 5 bites on the first fishing rod and 1 bite on the second. Therefore, in total, there are on average 6 bites on both fishing rods in these 5 minutes. Consequently, the average waiting time for the first bite is $\frac{5}{6}$ minutes.
Answer: 50 seconds.

## Grading Criteria

| Solution is correct and well-reasoned | 3 points |
| :--- | :---: |
| It is shown that on average there are 5 bites in 6 minutes, or an equivalent statement is proven | 1 point |
| Solution is incorrect or missing (including only the answer) | 0 points |