To solve this problem, we need to determine how long it will take for the fish to descend from -10.8 meters to -37.8 meters in depth.
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Determine the total depth the fish needs to descend:
The starting depth of the fish is -10.8 meters, and it needs to reach -37.8 meters.
\[ \text{Total descent} = \text{final depth} - \text{initial depth} \] \[ \text{Total descent} = -37.8 - (-10.8) \] \[ \text{Total descent} = -37.8 + 10.8 \] \[ \text{Total descent} = -27.0 \text{ meters} \]
Therefore, the fish needs to descend 27 meters.
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Calculate how many 2-minute intervals are needed for the descent:
The fish descends 1.5 meters every 2 minutes. To find out how many 2-minute intervals it takes to cover 27 meters, we can use the following formula:
\[ \text{Number of intervals} = \frac{\text{Total descent}}{\text{Descent per interval}} \] \[ \text{Number of intervals} = \frac{27.0}{1.5} \] \[ \text{Number of intervals} = 18 \]
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Calculate the total time taken:
Since each interval is 2 minutes, we multiply the number of intervals by the duration of each interval:
\[ \text{Total time (in minutes)} = \text{Number of intervals} \times \text{Interval duration} \] \[ \text{Total time} = 18 \times 2 = 36 \text{ minutes} \]
Conclusion:
It will take 36 minutes for the fish to reach a depth of -37.8 meters.
Explanation: This means that starting from a depth of -10.8 meters, the fish will take 36 minutes of swimming at a rate of 1.5 meters every 2 minutes to attain a depth of -37.8 meters in the water.