Multiply & Divide Rational Numbers Unit Test
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Question
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.(4 points)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
To solve this problem, we can use the equation:
depth = initial depth + (rate of descent * time)
Let's assign the values to the variables:
initial depth = -10.8 meters
rate of descent = 1.5 meters per 2 minutes
desired depth = -37.8 meters
We want to find the time it takes for the fish to reach the desired depth, so we can set up the equation:
-37.8 = -10.8 + (1.5 * time)
We can simplify this equation:
-37.8 = -10.8 + 1.5t
Now let's isolate t by subtracting -10.8 from both sides:
-37.8 - (-10.8) = 1.5t
-37.8 + 10.8 = 1.5t
-27 = 1.5t
Next, divide both sides by 1.5 to solve for t:
-27/1.5 = t
t = -18
The answer is -18.
This means it will take the fish 18 minutes to reach a depth of -37.8 meters.
To solve the word problem, we need to determine how long it will take for the fish to reach a depth of -37.8 meters. We know that the fish is currently at -10.8 meters and descends 1.5 meters every 2 minutes.
First, we need to find the difference in depth between the current depth and the desired depth:
-37.8 - (-10.8) = -37.8 + 10.8 = -27 meters
Next, we need to determine how many times the fish descends 1.5 meters in order to reach a depth of -27 meters. We can divide the difference in depth by 1.5:
-27 / 1.5 = -18
Since the fish descends 1.5 meters every 2 minutes, we need to multiply the number of times it descends by 2 to find the total time:
-18 * 2 = -36
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters. This means that after 36 minutes, the fish will be 37.8 meters below sea level.
To solve this word problem, we need to determine how long it will take for the fish to reach a depth of -37.8 meters.
We know that initially, the fish is swimming at -10.8 meters below sea level. Every 2 minutes, it descends another 1.5 meters.
To find the time it takes for the fish to reach a depth of -37.8 meters, we can use the equation:
Time = (Target Depth - Initial Depth)/Rate of Descent
In this case, the Target Depth is -37.8 meters, the Initial Depth is -10.8 meters, and the Rate of Descent is 1.5 meters every 2 minutes.
Now, let's calculate the time it will take for the fish to reach a depth of -37.8 meters:
Time = (-37.8 - (-10.8))/(1.5/2)
Time = (-37.8 + 10.8)/(1.5/2)
Time = -27/0.75
Time = -36
The fish will reach a depth of -37.8 meters in -36 minutes.
To explain what this answer means, it indicates that the fish will take 36 minutes to descend from its initial depth of -10.8 meters to a depth of -37.8 meters.