To find out how long it will take for the fish to reach a depth of -37.8 meters from its current depth of -10.8 meters by descending at a rate of 1.5 meters every 2 minutes, we can follow these steps:
-
Calculate the Total Depth Change: \[ \text{Total Depth Change} = \text{Target Depth} - \text{Current Depth} \] \[ \text{Total Depth Change} = -37.8 - (-10.8) = -37.8 + 10.8 = -27.0 \text{ meters} \]
-
Determine the Rate of Descent: The fish descends 1.5 meters every 2 minutes. To find the time taken to descend the total depth change, we need to calculate the number of descents needed to reach -37.8 meters:
\[ \text{Descent per interval} = 1.5 \text{ meters} \]
-
Calculate the Number of Intervals Needed: \[ \text{Number of Intervals} = \frac{\text{Total Depth Change}}{\text{Descent per interval}} = \frac{27.0}{1.5} \] \[ \text{Number of Intervals} = 18 \]
-
Calculate Total Time: Since each interval lasts 2 minutes, we multiply the number of intervals by the time per interval: \[ \text{Total Time} = \text{Number of Intervals} \times 2 \text{ minutes} \] \[ \text{Total Time} = 18 \times 2 = 36 \text{ minutes} \]
Conclusion: The fish will take 36 minutes to reach a depth of -37.8 meters. This means that starting from a depth of -10.8 meters, it will need to swim for 36 minutes, during which it descends at its regular pace until it reaches the target depth of -37.8 meters below sea level.
1 answer