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 mean
To find the time it will take for the fish to reach a depth of -37.8 meters, we need to calculate the number of 1.5 meter descents it will take to reach that depth.
First, let's find the difference between the current depth (-10.8 meters) and the target depth (-37.8 meters):
-37.8 - (-10.8) = -37.8 + 10.8 = -27 meters
Next, we divide the difference by the descent rate of 1.5 meters:
-27 / 1.5 = -18
The fish will need to make 18 descents of 1.5 meters to reach a depth of -37.8 meters.
Since the fish descends 1.5 meters every 2 minutes, we can multiply the number of descents by the time taken per descent:
18 x 2 = 36
Thus, it will take 36 minutes for the fish to reach a depth of -37.8 meters.
In sentence form, this answer means that the fish will need to descend 1.5 meters every 2 minutes for a total of 18 times, taking a total of 36 minutes, to reach a depth of -37.8 meters.
You can make it a bit easier to calculate by finding the overall distance needed to travel down (-37.8 - (-10.8)) and then dividing that amount by 1.5 meters, which will give the number of 2-minute blocks of time. Then multiply by 2 to find the total number of minutes.
To solve this problem, we can set up an equation using the given information.
Let "x" represent the time it takes for the fish to reach a depth of -37.8 meters.
We know that every 2 minutes, the fish descends another 1.5 meters. So, in "x" minutes, the fish will have descended a number of times equal to "x/2" (since every 2 minutes it descends 1.5 meters).
Given that the fish starts at -10.8 meters, we can set up the equation:
-10.8 + (x/2)(-1.5) = -37.8
To solve for "x", we can start by simplifying the equation:
-10.8 - 1.5x/2 = -37.8
Next, we can multiply both sides of the equation by 2 to eliminate the fraction:
-21.6 - 1.5x = -75.6
Now, let's isolate "x" by subtracting -21.6 from both sides:
-1.5x = -75.6 + 21.6
-1.5x = -54
Finally, divide both sides by -1.5 to solve for "x":
x = -54 / -1.5
x = 36
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters. This mean, after 36 minutes, the fish will be swimming 37.8 meters below sea level.
To solve this word problem, we need to find out how many times the fish descends 1.5 meters to reach a depth of -37.8 meters.
First, let's calculate the difference between the starting depth (-10.8 meters) and the target depth (-37.8 meters):
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters
We have a difference of -27 meters.
Next, let's divide the difference by the descent rate of 1.5 meters per 2 minutes to find out how many times the fish descends:
-27 meters / 1.5 meters per 2 minutes = -27/1.5 * 2/1 = -18 * 2/1 = -36
So, the fish needs to descend 36 times to reach a depth of -37.8 meters.
Now, we need to find the total time it takes for the fish to descend 36 times. Since the fish descends 1.5 meters every 2 minutes, we can multiply the number of descents by 2 to get the total time:
36 descents * 2 minutes per descent = 72 minutes
Therefore, it will take the fish 72 minutes to reach a depth of -37.8 meters.
In summary, the fish will reach a depth of -37.8 meters after 72 minutes of descending at a rate of 1.5 meters every 2 minutes.