Final answer:
In this case, the spider will catch the fly in 8 few minutes or 8 times the duration of each cycle.
Step-by-step explanation:
To determine how many minutes it will take for the spider to catch the fly, we can break down the scenario and calculate the time step by step:
1. The fly is sitting 9 meters high on the pool.
2. The spider climbs up 3 meters, reducing the distance between them to 6 meters (9 - 3 = 6).
3. The spider then falls back 2 meters, increasing the distance between them to 8 meters (6 + 2 = 8).
4. For each cycle, the spider reduces the distance by 1 meter (climbs 3 meters and falls 2 meters).
5. To determine the number of cycles needed to catch the fly, we can divide the remaining distance by the distance covered in each cycle:
8 meters / 1 meter = 8 cycles.
6. Since the spider goes through one cycle every few minutes, the total time it takes for the spider to catch the fly is 8 cycles * few minutes per cycle.
Therefore, the spider will catch the fly in 8 few minutes or 8 times the duration of each cycle.