To find out how long it will take the fish to reach a depth of -37.8 meters, we first need to determine how much deeper it needs to go from its current depth of -10.8 meters.
- Calculate the depth difference: \(-37.8 , \text{meters} - (-10.8 , \text{meters}) = -37.8 + 10.8 = -27.0 , \text{meters}\)
The fish needs to descend an additional 27.0 meters.
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The fish descends 1.5 meters every 2 minutes. To find out how many intervals of 2 minutes it will take to descend 27.0 meters, we divide the total depth needed by the depth it descends in each interval: \[ \text{Number of intervals} = \frac{27.0 , \text{meters}}{1.5 , \text{meters/interval}} = 18 , \text{intervals} \]
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Since each interval lasts 2 minutes, we multiply the number of intervals by the time per interval: \[ \text{Total time} = 18 , \text{intervals} \times 2 , \text{minutes/interval} = 36 , \text{minutes} \]
So, it will take the fish 36 minutes to reach a depth of -37.8 meters.