Let's break the problem down step by step:
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Starting Depth: The fish is currently at -10.8 meters.
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Target Depth: We need to find out how long it will take for the fish to reach -37.8 meters.
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Depth Change: Each time the fish swims for 2 minutes, it descends another 1.5 meters.
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Finding the Total Descent Needed: To find out how much deeper the fish needs to go, we subtract the starting depth from the target depth:
- Target Depth: -37.8 meters
- Starting Depth: -10.8 meters
\[ \text{Depth to descend} = -37.8 - (-10.8) = -37.8 + 10.8 = -27.0 \text{ meters} \]
So the fish needs to descend 27.0 meters to reach -37.8 meters.
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Finding Out How Many 2-Minute Intervals Are Needed: Since the fish descends 1.5 meters every 2 minutes, we divide the total depth it needs to descend by the amount 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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Calculating the Total Time: Now, we know it takes 2 minutes for each interval, so we multiply the number of intervals by the time for each interval:
\[ \text{Total time} = 18 \text{ intervals} \times 2 \text{ minutes/interval} = 36 \text{ minutes} \]
Final Answer: It will take the fish 36 minutes to reach the depth of -37.8 meters.
Explanation: This means that after swimming for 36 minutes, the fish will be much deeper in the water, going all the way down to 37.8 meters below sea level!