Question

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

Answer 1

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.