Question

The following word problem. A fish is swimming at -10.8, or 10.8 m 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

Answer 1

To find the time it will take for the fish to reach a depth of -37.8 meters, we can set up a basic equation.

Let "t" represent the time in minutes it takes for the fish to reach the desired depth.

The fish starts at -10.8 meters and descends at a rate of 1.5 meters per 2 minutes. Therefore, the depth of the fish after "t" minutes can be expressed as:

-10.8 + (1.5/2) * t

We can set this expression equal to the desired depth of -37.8 meters:

-10.8 + (1.5/2) * t = -37.8

Now, let's solve for "t":

(1.5/2) * t = -37.8 + 10.8

(1.5/2) * t = -27

Multiplying both sides by 2/1.5:

t = -27 * (2/1.5)

t = -36

Hence, the time it will take for the fish to reach a depth of -37.8 meters is -36 minutes.

However, since time cannot be negative in this context, we can conclude that it will take the fish 36 minutes to reach a depth of -37.8 meters.

Therefore, the fish will take 36 minutes to descend from its initial depth of -10.8 meters to a depth of -37.8 meters.