Question

Question
Solve the following word problem. A fish is swimming at −10.8
−
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
−
37.8
meters? Show your work and write a sentence to explain what your answer means.(4 points)

Answer 1

To solve the problem, we need to determine how long it will take for the fish to descend from a depth of \(-10.8\) meters to \(-37.8\) meters.

1. **Calculate the total distance the fish needs to descend:**
\[
\text{Distance to descend} = (-37.8) - (-10.8) = -37.8 + 10.8 = -27 \text{ meters}
\]

This means the fish needs to descend 27 meters.

2. **Determine how much the fish descends every 2 minutes:**
The fish descends 1.5 meters every 2 minutes.

3. **Find the total time needed to descend 27 meters:**
First, we calculate how many 2-minute intervals it takes to descend 27 meters.
\[
\text{Number of intervals} = \frac{\text{Total distance to descend}}{\text{Distance per interval}} = \frac{27}{1.5} = 18
\]

4. **Convert the number of intervals to time:**
Since each interval is 2 minutes long:
\[
\text{Total time} = \text{Number of intervals} \times 2 \text{ minutes} = 18 \times 2 = 36 \text{ minutes}
\]

**Final Answer:**
It will take the fish 36 minutes to reach a depth of \(-37.8\) meters.

**Explanation:**
This means that starting from a depth of \(-10.8\) meters, the fish will continue to swim downward for 36 minutes, reaching its target depth of \(-37.8\) meters after completing the descent.