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 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)
To solve this problem, we can use the formula:
Depth = initial depth + (rate of descent × time)
In this case, the initial depth is -10.8 meters and the rate of descent is 1.5 meters every 2 minutes. We need to find the time it takes for the fish to reach a depth of -37.8 meters.
Let's set up the equation and solve for time:
-37.8 = -10.8 + (1.5 × (time ÷ 2))
First, we can simplify the equation by multiplying 1.5 by 2:
-37.8 = -10.8 + 3 × time
Next, we subtract -10.8 from both sides of the equation to isolate the term with time:
-37.8 - (-10.8) = 3 × time
Simplifying further:
-37.8 + 10.8 = 3 × time
-27 = 3 × time
Now, divide both sides of the equation by 3 to solve for time:
time = -27 ÷ 3
time = -9 minutes
The fish will take 9 minutes to reach a depth of -37.8 meters.
This means that starting from -10.8 meters and descending 1.5 meters every 2 minutes, it will take the fish 9 minutes to reach a depth of -37.8 meters below sea level.