First, we need to determine how many meters the fish will descend to reach a depth of -24.5 meters from its current depth of -9.5 meters.
We can calculate this difference as follows:
\[ \text{Depth to reach} - (-9.5) = -24.5 - (-9.5) = -24.5 + 9.5 = -15 \text{ meters} \]
So, the fish needs to descend 15 meters to reach -24.5 meters.
Next, we know that the fish descends 1.5 meters every 3 minutes. To find out how many 3-minute intervals it will take to descend 15 meters, we can divide the total distance to descend by the distance it descends every interval:
\[ \text{Number of intervals} = \frac{\text{Total descent}}{\text{Descent per interval}} = \frac{15 \text{ meters}}{1.5 \text{ meters}} = 10 \]
Now we can find the total time taken by multiplying the number of intervals by the time per interval:
\[ \text{Total time} = \text{Number of intervals} \times \text{Time per interval} = 10 \times 3 \text{ minutes} = 30 \text{ minutes} \]
Thus, it will take the fish 30 minutes to reach a depth of -24.5 meters.
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