To determine how long it will take for the fish swimming at -10.8 meters below sea level to reach a depth of -37.8 meters, we start by calculating the total depth the fish needs to descend.
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Calculate the total depth change: \[ -37.8 , \text{meters (target depth)} - (-10.8 , \text{meters (current depth)}) = -37.8 + 10.8 = -27 , \text{meters} \] So, the fish needs to descend 27 meters.
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Determine the descent rate: The fish descends 1.5 meters every 2 minutes. We can convert this to a per minute rate: \[ \text{Descent rate} = \frac{1.5 , \text{meters}}{2 , \text{minutes}} = 0.75 , \text{meters per minute} \]
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Calculate the time required to descend 27 meters: To find the time \( t \) in minutes to descend 27 meters, we use the formula: \[ t = \frac{\text{Total depth to descend}}{\text{Descent rate}} \] Substituting in the values: \[ t = \frac{27 , \text{meters}}{0.75 , \text{meters per minute}} = 36 , \text{minutes} \]
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 take 36 minutes to swim down to -37.8 meters by continuously descending at a rate of 0.75 meters per minute.
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