Solve the following world problem of fish is swimming at -10.8 m or 10.8 m below sea level every two minutes it descends another 1.5 m. How long will it take for the fish to reach a depth of -37.8 m show your work, and write a sentence to explain what your answer means

1 answer

To determine how long it will take the fish to reach a depth of -37.8 m, we first need to calculate the total distance the fish needs to descend and how much it descends every two minutes.

  1. Initial depth of the fish: -10.8 m
  2. Target depth: -37.8 m

Step 1: Calculate the total descent needed

To find the total descent, we subtract the initial depth from the target depth:

\[ \text{Total descent} = \text{Target depth} - \text{Initial depth} \] \[ \text{Total descent} = -37.8, m - (-10.8, m) = -37.8, m + 10.8, m = -27, m \]

So, the fish needs to descend 27 meters.

Step 2: Determine how much the fish descends per time period

The fish descends 1.5 m every 2 minutes.

Step 3: Calculate how many 2-minute intervals are needed to descend 27 m

To find out how many intervals of 2 minutes are needed to reach a total descent of 27 m, we divide the total distance by the descent per interval:

\[ \text{Number of intervals} = \frac{\text{Total descent}}{\text{Descent per interval}} \] \[ \text{Number of intervals} = \frac{27, m}{1.5, m} = 18 \]

Step 4: Calculate the total time taken

Since each interval is 2 minutes, we multiply the number of intervals by the time for each interval:

\[ \text{Total time} = \text{Number of intervals} \times \text{Time per interval} \] \[ \text{Total time} = 18 \times 2, \text{minutes} = 36, \text{minutes} \]

Summary

Thus, the fish will take 36 minutes to reach a depth of -37.8 m from -10.8 m while descending 1.5 m every 2 minutes.

Sentence Explanation

This means that, starting from a depth of -10.8 m, the fish needs 36 minutes to descend to a depth of -37.8 m by continuously swimming down at a rate of 1.5 m every two minutes.