solve the following word problem. fish is swimming at negative 10.8 m, or 10.8 m below sea level. every 2 minutes it descends another 1.5 m. how long would it take for the fish to read a depth of -37.8 m? show your work and write a sentence to explain what your answer means.
To find out how long it would take for the fish to reach a depth of -37.8 m, we need to divide the change in depth by the descent rate.
Change in depth = -37.8 m - (-10.8 m) = -37.8 m + 10.8 m = -27 m
Descent rate = 1.5 m/2 minutes = 0.75 m/minute
Time = Change in depth / Descent rate = -27 m / 0.75 m/min = -36 minutes
Since time cannot be negative, we can conclude that it would take the fish 36 minutes to reach a depth of -37.8 m.
Explanation: The fish is swimming at a depth of -10.8 m and descends 1.5 m every 2 minutes. To reach a depth of -37.8 m, the fish would need to descend an additional 27 m. At a descent rate of 0.75 m/minute, it would take the fish 36 minutes to reach that depth.
To solve this problem, we can use a simple equation to calculate the time it would take for the fish to reach a depth of -37.8 m:
Depth = Initial Depth + (Rate × Time)
where:
Initial Depth = -10.8 m
Rate = -1.5 m/2 minutes (as the fish descends another 1.5 m every 2 minutes)
Depth = -37.8 m
Let's substitute the values into the equation:
-37.8 m = -10.8 m + (-1.5 m/2 min) × Time
First, let's simplify the equation:
-37.8 m + 10.8 m = (-1.5 m/2 min) × Time
-27 m = (-1.5 m/2 min) × Time
Next, let's solve for Time by dividing both sides of the equation by (-1.5 m/2 min):
Time = (-27 m) / (-1.5 m/2 min)
Time = (2 min/(-1.5 m)) × (-27 m)
Time = (-2/1.5) × 27
Time ≈ -36 minutes
So, it would take approximately 36 minutes for the fish to reach a depth of -37.8 m.
This negative value indicates that the fish is descending below 0 (sea level). Therefore, the sentence explaining the answer would be:
"The fish would take approximately 36 minutes to descend to a depth of -37.8 m, which is 37.8 m below sea level."
To solve this word problem, we need to find out how many times the fish descends by 1.5 m until it reaches a depth of -37.8 m.
Let's set up an equation to represent this situation:
Starting Depth: -10.8 m
Target Depth: -37.8 m
Rate of Descent per 2 minutes: 1.5 m
Let's denote the number of times the fish descends by "n".
After n descents of 1.5 m, the total depth change would be 1.5m x n, which should equal the target depth of -37.8 m.
1.5n = -37.8
Now divide both sides of the equation by 1.5:
n = -37.8 / 1.5
n = -25.2
Since the number of descents can't be negative, we would consider the absolute value of n.
|n| = 25.2
Therefore, it would take the fish approximately 25 descents of 1.5 m each (over 50 minutes) to reach a depth of -37.8 m.
In simpler terms, it would take the fish around 50 minutes to dive down about 37.8 meters below sea level.