To solve the problem, we need to find out how long it will take for the fish to reach a depth of −37.8 meters, starting from −10.8 meters and descending 1.5 meters every 2 minutes.
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Determine the total depth the fish needs to descend.
Starting depth: -10.8 meters
Target depth: -37.8 metersTo find the total distance the fish needs to descend, we can subtract the starting depth from the target depth:
\[ \text{Total depth to descend} = \text{Target depth} - \text{Starting depth} \]
\[ = -37.8 - (-10.8) \]
\[ = -37.8 + 10.8 \]
\[ = -27.0 \text{ meters} \]
This means the fish needs to descend 27.0 meters to reach -37.8 meters.
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Determine how many 2-minute intervals of descent are needed.
The fish descends 1.5 meters every 2 minutes. To find out how many intervals of 1.5 meters are needed to descend 27.0 meters, we can divide the total descent by the distance per interval:
\[ \text{Number of intervals} = \frac{\text{Total depth to descend}}{\text{Depth per interval}} \]
\[ = \frac{27.0 \text{ meters}}{1.5 \text{ meters/interval}} \]
\[ = 18 \text{ intervals} \]
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Convert intervals to time.
Since each interval takes 2 minutes, we can find the total time taken by multiplying the number of intervals by the time per interval:
\[ \text{Total time} = \text{Number of intervals} \times \text{Time per interval} \]
\[ = 18 \times 2 \text{ minutes} \]
\[ = 36 \text{ minutes} \]
Answer: It will take the fish 36 minutes to reach a depth of -37.8 meters.
This means that starting from a depth of 10.8 meters below sea level, the fish will take 36 minutes to further descend to a depth of 37.8 meters below sea level.