Question

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 means.(4 points)

Answer 1

To find out how long it will take for the fish to reach a depth of -37.8 meters, we start with the initial depth of -10.8 meters and determine how much deeper the fish needs to descend.

1. **Calculate the total depth change needed:**

\[
\text{Depth change} = \text{Final depth} - \text{Initial depth}
\]
\[
\text{Depth change} = -37.8 - (-10.8) = -37.8 + 10.8 = -27.0 \, \text{meters}
\]

The fish needs to descend a total of 27.0 meters.

2. **Determine how much the fish descends every 2 minutes:**

The fish descends 1.5 meters every 2 minutes.

3. **Calculate the total time required to descend 27.0 meters:**

We can find the time by dividing the total depth change needed by the distance descended every 2 minutes.

First, find how many 1.5 meter intervals are in 27.0 meters:

\[
\text{Number of intervals} = \frac{27.0 \, \text{meters}}{1.5 \, \text{meters}} = 18
\]

Each interval takes 2 minutes, so:

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

**Conclusion:**

It will take the fish 36 minutes to reach a depth of -37.8 meters from its current position at -10.8 meters. This means that the fish will continue to swim deeper below sea level for a total of 36 minutes until it reaches the target depth.