Solve the following word problem a fish is swimming at -10.8 m or 10.8 m below sea level every two minutes it descends another one and a half meters. How long will it take for the fish to reach a depth of -37.8 m show your work and write a sentence to explain what your answer means.
To find how long it will take for the fish to reach a depth of -37.8 m, we need to determine how many times it will descend by 1.5 m before reaching that depth.
The difference in depth between the starting point and the desired depth is -37.8 m - (-10.8 m) = -37.8 m + 10.8 m = -27 m.
Since the fish descends by 1.5 m every two minutes, the number of descents it will make is -27 m / 1.5 m = -18.
Therefore, it will take the fish 18 * 2 = 36 minutes to reach a depth of -37.8 m.
This means that the fish will take 36 minutes to swim 10.8 m below sea level to a depth of -37.8 m.
To find how long it will take for the fish to reach a depth of -37.8 m, we can set up an equation.
Let's define t as the number of minutes it takes for the fish to reach the desired depth of -37.8 m.
The initial depth of the fish is -10.8 m below sea level, and every two minutes, it descends another 1.5 meters.
So, after t minutes, the fish will have descended "1.5 * (t/2)" meters.
Therefore, the equation to solve is:
-10.8 + 1.5 * (t/2) = -37.8
We can simplify this equation:
-10.8 + 0.75t = -37.8
Now, let's solve for t:
-10.8 + 0.75t = -37.8
0.75t = -37.8 + 10.8
0.75t = -27
Divide both sides by 0.75 to isolate t:
t = -27 / 0.75
t = -36
Since time cannot be negative, we can ignore the negative solution.
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 m.
The answer indicates that it will take the fish 36 minutes to descend from its initial depth of -10.8 m to a depth of -37.8 m, given that it descends 1.5 meters every two minutes.
To solve this word problem, we can set up an equation based on the information given.
Let's use "t" to represent the time in minutes and "d" to represent the distance in meters below sea level.
The initial depth of the fish is -10.8 m, and every two minutes, it descends another 1.5 meters. So, after "t" minutes, the fish will have descended a total of (1.5 * t) meters.
The equation is:
-10.8 + (1.5 * t) = -37.8
Now, let's solve the equation to find the value of "t".
-10.8 + 1.5t = -37.8
1.5t = -37.8 + 10.8
1.5t = -27
t = -27 / 1.5
t = -18
Therefore, it will take the fish approximately 18 minutes to reach a depth of -37.8 meters.
This means that over time, as the fish descends further, it will take 18 minutes for the fish to reach a depth of -37.8 meters below sea level.