Question

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 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 need to determine the total depth the fish needs to descend from its starting depth of -10.8 meters to -37.8 meters.

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

\[
\text{Total depth change} = \text{Final depth} - \text{Starting depth}
\]
\[
\text{Total depth change} = -37.8 - (-10.8)
\]
\[
\text{Total depth change} = -37.8 + 10.8 = -27.0 \text{ meters}
\]

The fish needs to descend 27.0 meters.

2. **Determine the rate of descent:**

The fish descends 1.5 meters every 2 minutes. Therefore, we can calculate how many meters it descends in one minute:

\[
\text{Rate of descent} = \frac{1.5 \text{ meters}}{2 \text{ minutes}} = 0.75 \text{ meters per minute}
\]

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

We can now find out how long it will take to descend that total depth:

\[
\text{Time} = \frac{\text{Total depth change}}{\text{Rate of descent}}
\]
\[
\text{Time} = \frac{27.0 \text{ meters}}{0.75 \text{ meters per minute}}
\]
\[
\text{Time} = 36 \text{ minutes}
\]

4. **Conclusion:**

It will take the fish 36 minutes to reach a depth of -37.8 meters.

**Final sentence:** The fish will take 36 minutes to swim down from a depth of -10.8 meters to -37.8 meters, descending at a rate of 1.5 meters every 2 minutes.