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. pls make the equation

Answer 1

To find out how long it will take for the fish to descend from -10.8 meters to -37.8 meters, we can start by defining the variables and setting up the equation.

1. **Initial Depth (D_initial)**: -10.8 meters
2. **Final Depth (D_final)**: -37.8 meters
3. **Depth Increase per Time Period (d)**: The fish descends 1.5 meters every 2 minutes.

**First**, we need to determine the total depth change required for the fish to reach its final depth:

\[
\text{Total depth change} = D_{final} - D_{initial} = -37.8 - (-10.8)
\]

Calculating:

\[
D_{final} - D_{initial} = -37.8 + 10.8 = -27.0 \text{ meters}
\]

So the fish needs to descend 27 meters to reach a depth of -37.8 meters.

**Next**, we need to find out how many 1.5 meter descents are needed to reach this total depth change:

\[
\text{Number of descents (n)} = \frac{\text{Total depth change}}{\text{Depth increase per time period}} = \frac{27.0}{1.5}
\]

Calculating:

\[
n = \frac{27.0}{1.5} = 18
\]

This means the fish needs to make 18 descents of 1.5 meters.

**Finally**, since each descent takes 2 minutes, we can find the total time (T) in minutes:

\[
T = n \times (2 \text{ minutes}) = 18 \times 2 = 36 \text{ minutes}
\]

**Conclusion**: It will take the fish 36 minutes to reach a depth of -37.8 meters. This means that starting from a depth of -10.8 meters, the fish will take 36 minutes descending at a rate of 1.5 meters every 2 minutes to reach the target depth.