To find out how long it will take for the fish to reach a depth of -37.8 meters, we start with the initial depth of -10.8 meters and determine how much deeper the fish needs to descend.
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Calculate the total depth change needed:
\[ \text{Depth change} = \text{Final depth} - \text{Initial depth} \] \[ \text{Depth change} = -37.8 - (-10.8) = -37.8 + 10.8 = -27.0 , \text{meters} \]
The fish needs to descend a total of 27.0 meters.
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Determine how much the fish descends every 2 minutes:
The fish descends 1.5 meters every 2 minutes.
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Calculate the total time required to descend 27.0 meters:
We can find the time by dividing the total depth change needed by the distance descended every 2 minutes.
First, find how many 1.5 meter intervals are in 27.0 meters:
\[ \text{Number of intervals} = \frac{27.0 , \text{meters}}{1.5 , \text{meters}} = 18 \]
Each interval takes 2 minutes, so:
\[ \text{Total time} = \text{Number of intervals} \times \text{Time per interval} \] \[ \text{Total time} = 18 \times 2 , \text{minutes} = 36 , \text{minutes} \]
Conclusion:
It will take the fish 36 minutes to reach a depth of -37.8 meters from its current position at -10.8 meters. This means that the fish will continue to swim deeper below sea level for a total of 36 minutes until it reaches the target depth.