To solve this problem, we need to first determine how much deeper the fish needs to descend to reach a depth of -37.8 meters from its current depth of -10.8 meters.
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Calculate the distance the fish needs to descend: \[ \text{Depth difference} = \text{Final depth} - \text{Current depth} \] \[ \text{Depth difference} = -37.8 - (-10.8) = -37.8 + 10.8 = -27 , \text{meters} \]
So, the fish needs to descend 27 meters to reach -37.8 meters.
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Determine how many 1.5 meter descents it takes to cover 27 meters: Since the fish descends 1.5 meters every 2 minutes, we can find the number of descents needed: \[ \text{Number of descents} = \frac{\text{Total descent needed}}{\text{Descent per interval}} = \frac{27}{1.5} = 18 \]
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Calculate the total time taken for these descents: Since each descent takes 2 minutes: \[ \text{Total time} = \text{Number of descents} \times \text{Time per descent} = 18 \times 2 = 36 , \text{minutes} \]
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Conclusion: The fish will take 36 minutes to reach a depth of -37.8 meters.
In summary, starting from -10.8 meters, it will take the fish 36 minutes to descend to -37.8 meters by swimming down 1.5 meters every 2 minutes.