The following word problem. A fish is swimming at -10.8, or 10.8 m 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? Show your work and write a sentence to explain what your answer means
To find the time it will take for the fish to reach a depth of -37.8 meters, we can set up a basic equation.
Let "t" represent the time in minutes it takes for the fish to reach the desired depth.
The fish starts at -10.8 meters and descends at a rate of 1.5 meters per 2 minutes. Therefore, the depth of the fish after "t" minutes can be expressed as:
-10.8 + (1.5/2) * t
We can set this expression equal to the desired depth of -37.8 meters:
-10.8 + (1.5/2) * t = -37.8
Now, let's solve for "t":
(1.5/2) * t = -37.8 + 10.8
(1.5/2) * t = -27
Multiplying both sides by 2/1.5:
t = -27 * (2/1.5)
t = -36
Hence, the time it will take for the fish to reach a depth of -37.8 meters is -36 minutes.
However, since time cannot be negative in this context, we can conclude that it will take the fish 36 minutes to reach a depth of -37.8 meters.
Therefore, the fish will take 36 minutes to descend from its initial depth of -10.8 meters to 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 need to calculate the number of 1.5-meter descents required to reach that depth.
First, we find the difference between the starting depth (-10.8 meters) and the target depth (-37.8 meters): -37.8 - (-10.8) = -37.8 + 10.8 = -27 meters.
Next, we divide this difference by the descent rate of 1.5 meters per 2 minutes: -27 / 1.5 = -18.
The negative sign indicates that the fish is descending. Hence, the fish will take 18 intervals of 2 minutes each to reach a depth of -37.8 meters.
In conclusion, it will take the fish 36 minutes (18 x 2) to reach a depth of -37.8 meters.
To solve this problem, we need to determine how many 2-minute intervals it will take the fish to reach a depth of -37.8 meters.
First, let's find the difference between the initial depth (-10.8 meters) and the target depth (-37.8 meters):
Difference = Target depth - Initial depth
Difference = (-37.8 meters) - (-10.8 meters)
Difference = -37.8 meters + 10.8 meters
Difference = -27 meters
Next, we need to find out how many 1.5-meter descents the fish makes in each 2-minute interval. We divide the difference by the descent rate:
Descent rate = 1.5 meters per 2 minutes
Number of descents = Difference / Descent rate
Number of descents = -27 meters / 1.5 meters per 2 minutes
Now, we can calculate the number of descents:
Number of descents = -27 meters / 1.5 meters per 2 minutes
Number of descents = -27 meters / 1.5 meters * 2 minutes per descent
Number of descents = -27 meters / 3 meters
Number of descents = -9
The result is -9, indicating that the fish will make 9 two-minute descents to reach the depth of -37.8 meters.
Therefore, it will take the fish 9 * 2 = 18 minutes to reach a depth of -37.8 meters.
In conclusion, the fish will take 18 minutes to reach a depth of -37.8 meters.