To find out how long it will take for the fish to descend from -10.8 meters to -37.8 meters, we can start by defining the variables and setting up the equation.
- Initial Depth (D_initial): -10.8 meters
- Final Depth (D_final): -37.8 meters
- Depth Increase per Time Period (d): The fish descends 1.5 meters every 2 minutes.
First, we need to determine the total depth change required for the fish to reach its final depth:
\[ \text{Total depth change} = D_{final} - D_{initial} = -37.8 - (-10.8) \]
Calculating:
\[ D_{final} - D_{initial} = -37.8 + 10.8 = -27.0 \text{ meters} \]
So the fish needs to descend 27 meters to reach a depth of -37.8 meters.
Next, we need to find out how many 1.5 meter descents are needed to reach this total depth change:
\[ \text{Number of descents (n)} = \frac{\text{Total depth change}}{\text{Depth increase per time period}} = \frac{27.0}{1.5} \]
Calculating:
\[ n = \frac{27.0}{1.5} = 18 \]
This means the fish needs to make 18 descents of 1.5 meters.
Finally, since each descent takes 2 minutes, we can find the total time (T) in minutes:
\[ T = n \times (2 \text{ minutes}) = 18 \times 2 = 36 \text{ minutes} \]
Conclusion: 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, the fish will take 36 minutes descending at a rate of 1.5 meters every 2 minutes to reach the target depth.
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