To solve the problem, we need to determine how long it will take for the fish to descend from a depth of \(-10.8\) meters to \(-37.8\) meters.
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Calculate the total distance the fish needs to descend: \[ \text{Distance to descend} = (-37.8) - (-10.8) = -37.8 + 10.8 = -27 \text{ meters} \]
This means the fish needs to descend 27 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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Find the total time needed to descend 27 meters: First, we calculate how many 2-minute intervals it takes to descend 27 meters. \[ \text{Number of intervals} = \frac{\text{Total distance to descend}}{\text{Distance per interval}} = \frac{27}{1.5} = 18 \]
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Convert the number of intervals to time: Since each interval is 2 minutes long: \[ \text{Total time} = \text{Number of intervals} \times 2 \text{ minutes} = 18 \times 2 = 36 \text{ minutes} \]
Final Answer: It will take the fish 36 minutes to reach a depth of \(-37.8\) meters.
Explanation: This means that starting from a depth of \(-10.8\) meters, the fish will continue to swim downward for 36 minutes, reaching its target depth of \(-37.8\) meters after completing the descent.
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