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 + 1.5x = -37.8
Where x represents the number of 2-minute intervals.
To solve for x, we need to isolate it on one side of the equation. First, we can subtract -10.8 from both sides:
1.5x = -37.8 - (-10.8)
1.5x = -37.8 + 10.8
1.5x = -27
Next, we divide both sides by 1.5 to solve for x:
x = -27 / 1.5
x = -18
Therefore, it will take the fish 18 intervals of 2 minutes each to reach a depth of -37.8 meters.
This means that it will take 36 minutes for the fish to reach a depth of -37.8 meters below sea level.
To find out how long it will take for the fish to reach a depth of -37.8 meters, we can subtract the initial depth from the target depth and divide it by the rate of descent.
Initial depth: -10.8 meters
Target depth: -37.8 meters
Rate of descent: 1.5 meters per 2 minutes
Change in depth: -37.8 meters - (-10.8 meters) = -27 meters
Time required: (-27 meters) / (1.5 meters per 2 minutes) = -18 minutes
The fish will take 18 minutes to reach a depth of -37.8 meters. Since the time is negative, it means the fish will reach the target depth 18 minutes before the given reference time (e.g., the starting time).
To find out how long it will take for the fish to reach a depth of -37.8 meters, we need to calculate the number of descents the fish needs to make and then multiply it by the time taken for each descent.
First, let's calculate the difference in depth between the starting point (-10.8 meters) and the target depth (-37.8 meters):
Difference = Target depth - Starting depth
Difference = (-37.8 meters) - (-10.8 meters)
Difference = -37.8 meters + 10.8 meters
Difference = -27 meters
Next, we need to calculate the number of descents the fish needs to make to cover this difference. Since the fish descends 1.5 meters every 2 minutes, we can find the number of descents by dividing the difference by the descent distance:
Number of descents = Difference / Descent distance
Number of descents = -27 meters / 1.5 meters
Number of descents = -18
To convert the negative number of descents into positive, we take the absolute value:
Number of descents = | -18 |
Number of descents = 18
Now, we know the fish needs to make 18 descents. Since the fish descends 1.5 meters in each 2-minute interval, the time taken to reach a depth of -37.8 meters would be:
Time taken = Number of descents × Time per descent
Time taken = 18 × 2 minutes
Time taken = 36 minutes
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
In simpler terms, this means that the fish will need to descend 18 times, with each descent taking 2 minutes. So, after 36 minutes, the fish will have reached a depth of -37.8 meters.