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 the time it takes for the fish to reach a depth of -37.8 meters, we can set up an equation:
-10.8 - 1.5t = -37.8
First, let's simplify the equation:
-1.5t = -37.8 + 10.8
-1.5t = -27
Next, let's solve for t (the time):
t = (-27) / (-1.5)
t = 18
Therefore, it will take the fish 18 minutes to reach a depth of -37.8 meters.
This means that every 2 minutes, the fish descends 1.5 meters. So, if it took 18 minutes to reach a depth of -37.8 meters, it descended a total of 1.5 meters every 2 minutes for a total of 18/2 = 9 times.
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.
Let "x" represent the number of times the fish descends another 1.5 meters.
The total descent in meters can be calculated as: -10.8 meters + (1.5 meters * x).
We want the fish to reach a depth of -37.8 meters, so we set up the equation:
-10.8 + (1.5 * x) = -37.8
To solve this equation, we can first subtract -10.8 from both sides of the equation:
1.5 * x = -37.8 - (-10.8)
1.5 * x = -27
Next, we divide both sides of the equation by 1.5 to isolate the "x" term:
x = -27 / 1.5
x = -18
Therefore, it will take the fish 18 descents of 1.5 meters each to reach a depth of -37.8 meters.
To find the time it takes for the fish to reach this depth, we multiply the number of descents (18) by the time it takes for each descent (2 minutes):
Time = 18 * 2
Time = 36 minutes
So, it will take the fish 36 minutes to reach a depth of -37.8 meters. This means that after descending 1.5 meters every 2 minutes, the fish will reach a depth of -37.8 meters after approximately 36 minutes of continuous descent.
To solve this word problem, we can use the information given and break it down into steps.
Step 1: Calculate the difference in depth between the starting point and the desired depth.
The starting depth is -10.8 meters, and the desired depth is -37.8 meters. To find the difference, we subtract the starting depth from the desired depth:
Difference = -37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters.
Step 2: Determine the number of 1.5 meter descents needed to cover the difference in depth.
Since the fish descends 1.5 meters every 2 minutes, we divide the difference in depth by 1.5:
Number of descents = Difference / 1.5 = -27 meters / 1.5 = -18 descents.
Step 3: Calculate the time it will take for the fish to reach the desired depth.
Since the fish descends 1.5 meters every 2 minutes, we need to multiply the number of descents by 2 to get the total time in minutes:
Time in minutes = Number of descents * 2 = -18 descents * 2 = -36 minutes.
Thus, it will take the fish approximately 36 minutes to reach a depth of -37.8 meters.
Explanation: The answer means that the fish will take 36 minutes to swim from a depth of -10.8 meters to a depth of -37.8 meters, descending 1.5 meters every 2 minutes.