Solve the following word problem. 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? Show your work and write a sentence to explain what your answer means
To find out how long it will take for the fish to reach a depth of -37.8 meters, we can set up an equation:
-10.8 meters + (-1.5 meters * t) = -37.8 meters
To simplify the equation, we can add 10.8 meters to both sides:
-1.5 meters * t = -37.8 meters + 10.8 meters
-1.5 meters * t = -27 meters
Now, we can solve for t by dividing both sides of the equation by -1.5 meters:
t = (-27 meters) / (-1.5 meters)
t = 18
Therefore, it will take the fish 18 minutes to reach a depth of -37.8 meters.
This means that after 18 minutes, the fish will have descended from its initial depth of -10.8 meters to a depth of -37.8 meters.
To solve this problem, we can use the equation:
Depth = Initial Depth + (Rate of Descent * Time)
Let's denote the initial depth as x and the rate of descent as r. In this case, x = -10.8 meters and r = -1.5 meters per 2 minutes.
We want to find the time it takes for the fish to reach a depth of -37.8 meters. Denoting the time as t, we have:
-37.8 = -10.8 + (-1.5/2) * t
Simplifying the equation:
-37.8 + 10.8 = (-1.5/2) * t
-27 = -0.75 * t
Dividing both sides by -0.75:
t = 27 / 0.75
t = 36
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
Explanation: The answer means that after swimming for 36 minutes, the fish will reach a depth of -37.8 meters below sea level, starting from -10.8 meters below sea level.
To solve this word problem, we need to find out how many times the fish descends by 1.5 meters until it reaches a depth of -37.8 meters.
We can start by subtracting the initial depth of the fish (-10.8 meters) from the target depth (-37.8 meters):
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters
Next, we need to determine how many times the fish descends by 1.5 meters in order to reach a depth of -27 meters. We can find this by dividing the change in depth (-27 meters) by the descent rate (1.5 meters) per 2 minutes:
-27 meters ÷ 1.5 meters = -18
The result is -18, which means the fish must descend 18 times by 1.5 meters to reach a depth of -37.8 meters.
Finally, since the fish descends by 1.5 meters every 2 minutes, we need to determine the total time it takes for 18 descents. Since each descent takes 2 minutes, the total time would be:
18 descents × 2 minutes per descent = 36 minutes
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
In summary, it will take the fish 36 minutes to reach a depth of -37.8 meters, descending at a rate of 1.5 meters every 2 minutes.