To determine how long it will take for the fish to reach a depth of -24.5 meters, we first need to identify how far the fish needs to descend from its current depth of -9.5 meters.
- Calculate the total descent required: \[ \text{Depth to reach} = -24.5 \text{ meters} \] \[ \text{Current depth} = -9.5 \text{ meters} \] \[ \text{Descent required} = -24.5 - (-9.5) = -24.5 + 9.5 = -15 \text{ meters} \]
So, the fish needs to descend 15 meters.
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Calculate the rate of descent: The fish descends 1.5 meters every 3 minutes.
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Calculate how many 3-minute intervals are needed to descend 15 meters: To find out how many intervals are needed, we divide the total descent by the distance descended in each interval: \[ \text{Intervals} = \frac{\text{Descent required}}{\text{Descent per interval}} = \frac{15 \text{ meters}}{1.5 \text{ meters}} = 10 \text{ intervals} \]
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Calculate the total time needed: Since each interval takes 3 minutes, the total time required is: \[ \text{Total time} = 10 \text{ intervals} \times 3 \text{ minutes per interval} = 30 \text{ minutes} \]
Thus, it will take the fish 30 minutes to reach a depth of -24.5 meters.