solve the following word problem. A fish is swimming at -10.8, 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? Show your work and write a sentence to explain what your answer means
To solve this problem, we can set up an equation to represent the fish's depth at any given time. Let's define "t" as the time in minutes and "d" as the depth in meters.
The initial depth is -10.8 meters, and every 2 minutes the fish descends another 1.5 meters. Therefore, the equation that represents the depth at time "t" is: d = -10.8 - 1.5(t/2).
We want to find the time "t" it takes for the fish to reach a depth of -37.8 meters. So we substitute "-37.8" for "d" in the equation and solve for "t":
-37.8 = -10.8 - 1.5(t/2)
-37.8 + 10.8 = -1.5(t/2)
-27 = -1.5(t/2)
-27 = -0.75t
t = (-27) / (-0.75)
t = 36.
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
This means that after 36 minutes of swimming at a rate of descending 1.5 meters every 2 minutes, the fish will be at a depth of -37.8 meters below sea level.
To solve this word problem, we can set up an equation to represent the situation.
Let's assume the time taken by the fish to reach a depth of -37.8 meters is represented by 't' minutes.
In every 2 minutes, the fish descends an additional 1.5 meters. So, in 't' minutes, the fish would have descended (t/2) * 1.5 meters.
To find the total depth reached by the fish, we can add the initial depth (-10.8 meters) and the additional depth descended: -10.8 + (t/2) * 1.5.
Setting this equal to the target depth of -37.8 meters gives us the equation:
-10.8 + (t/2) * 1.5 = -37.8
To solve for 't,' we can start by isolating the variable:
(t/2) * 1.5 = -37.8 + 10.8
(t/2) * 1.5 = -27
Next, simplify the equation:
t/2 = -27 / 1.5
t/2 = -18
Finally, multiply both sides by 2 to solve for 't':
t = -18 * 2
t = -36
The negative time value indicates the fish will reach a depth of -37.8 meters in the past, 36 minutes ago. This means the fish had already reached that depth 36 minutes ago.
Therefore, the fish took 36 minutes to reach a depth of -37.8 meters.
To solve this word problem, we can set up an equation to represent the descending depth of the fish over time. Let's suppose the time taken for the fish to reach a certain depth is represented by 't' minutes.
Since the fish descends 1.5 meters every 2 minutes, we can express its descent as: (1.5 meters / 2 minutes) * t minutes, or (1.5/2) * t.
Now, the initial depth of the fish is -10.8 meters. So, the equation becomes:
-10.8 meters + (1.5/2) * t = -37.8 meters.
Next, we can solve this equation to find the value of 't'.
Adding 10.8 to both sides of the equation, we get:
(1.5/2) * t = -37.8 meters + 10.8 meters,
(1.5/2) * t = -27 meters.
To isolate 't', we multiply both sides of the equation by 2/1.5, or 4/3:
t = (-27 meters) * (4/3),
t = -36 minutes.
The solution to the equation is t = -36 minutes.
However, since time cannot be negative in this context, the answer is not meaningful. In other words, it does not make sense for the fish to reach a depth of -37.8 meters in a negative time.
Therefore, there is no solution to this word problem, and the fish cannot reach a depth of -37.8 meters.