A fish is swimming at −10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of -37.8 meters?
The fish descends 1.5 meters every 2 minutes, so the number of 1.5 meter increments it takes to reach the desired depth is -37.8 meters / 1.5 meters = <<37.8/1.5=25.2>>25.2 increments.
Since each increment takes 2 minutes, the fish will take a total of 25.2 increments * 2 minutes/increment = <<25.2*2=50.4>>50.4 minutes to reach a depth of -37.8 meters. Answer: \boxed{50.4}.
To find the time it will take for the fish to reach a depth of -37.8 meters, we can calculate the number of times it needs to descend 1.5 meters to reach that depth.
The initial depth of the fish is -10.8 meters, and it needs to reach -37.8 meters. The difference in depth is 37.8 - 10.8 = 27 meters.
The fish descends 1.5 meters every 2 minutes. So, the number of times it needs to descend by 1.5 meters is 27 / 1.5 = 18 times.
Since the fish descends every 2 minutes, it will take 2 minutes per descent. So, the total time it will take for the fish to reach a depth of -37.8 meters is 18 * 2 = <<18*2=36>>36 minutes.
To find out how long it will take for the fish to reach a depth of -37.8 meters, we need to figure out how many 1.5-meter descents the fish has to make.
First, we need to find the difference between the current depth (-10.8 meters) and the target depth (-37.8 meters):
Difference = Target depth - Current depth
Difference = -37.8 meters - (-10.8 meters)
Difference = -37.8 meters + 10.8 meters
Difference = -27 meters
Next, we divide the difference by the descent rate of 1.5 meters every 2 minutes to find out how many 1.5-meter descents the fish has to make:
Number of descents = Difference / Descent rate
Number of descents = -27 meters / 1.5 meters
Number of descents ≈ -18
Since we can't have a negative number of descents in this context, we take the absolute value and round up to the nearest whole number:
Number of descents = |-18| ≈ 18
Now, we multiply the number of descents by the time it takes for each descent (2 minutes) to find out the total time it will take for the fish to reach a depth of -37.8 meters:
Total time = Number of descents × Time per descent
Total time = 18 descents × 2 minutes per descent
Total time = 36 minutes
Therefore, it will take the fish approximately 36 minutes to reach a depth of -37.8 meters.