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 minutes it takes to descend by 37.8 meters is −37.8 / −1.5 = <<37.8/1.5=25.2>>25.2 minutes. Answer: \boxed{25.2}.
To find out how long it will take for the fish to reach a depth of −37.8 meters, we can use the formula:
Time = (Depth of the target − Initial depth) ÷ Descent rate
Here, the initial depth is −10.8 meters, the target depth is −37.8 meters, and the descent rate is 1.5 meters per 2 minutes.
Plugging in these values into the formula, we get:
Time = (−37.8 m − (−10.8 m)) ÷ 1.5 m/2 min
Simplifying:
Time = (−37.8 m + 10.8 m) ÷ (1.5 m/2 min)
Time = −27 m ÷ (1.5 m/2 min)
Time = −27 m × (2 min/1.5 m)
Time = −27 m × (2/1.5) min
Time = −27 m × 1.333 min
Time = −35.9916 min
Since time cannot be negative, we take the absolute value:
Time ≈ 35.9916 min
So, it will take approximately 35.9916 minutes for the fish to reach a depth of −37.8 meters.
To find out how long it will take for the fish to reach a depth of -37.8 meters, we can calculate the number of descents the fish needs to make and then multiply that by the time required for each descent.
First, let's determine the difference between the current depth of the fish (-10.8 meters) and the target depth (-37.8 meters):
Difference in depth = Target depth - Current depth
Difference in depth = -37.8 meters - (-10.8 meters)
Difference in depth = -37.8 meters + 10.8 meters
Difference in depth = -27 meters
Since the fish descends 1.5 meters every 2 minutes, we can calculate the number of descents required to cover the difference in depth:
Number of descents = Difference in depth / Depth covered per descent
Number of descents = -27 meters / 1.5 meters
Number of descents ≈ 18
Now, we know that the fish takes 2 minutes to make a descent of 1.5 meters. So to find the total time required, we can multiply the number of descents by the time per descent:
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.