Question

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

Answer 1

To solve this problem, we need to first determine how much deeper the fish needs to descend to reach a depth of -37.8 meters from its current depth of -10.8 meters.

1. **Calculate the distance the fish needs to descend:**
\[
\text{Depth difference} = \text{Final depth} - \text{Current depth}
\]
\[
\text{Depth difference} = -37.8 - (-10.8) = -37.8 + 10.8 = -27 \, \text{meters}
\]

So, the fish needs to descend **27 meters** to reach -37.8 meters.

2. **Determine how many 1.5 meter descents it takes to cover 27 meters:**
Since the fish descends 1.5 meters every 2 minutes, we can find the number of descents needed:
\[
\text{Number of descents} = \frac{\text{Total descent needed}}{\text{Descent per interval}} = \frac{27}{1.5} = 18
\]

3. **Calculate the total time taken for these descents:**
Since each descent takes 2 minutes:
\[
\text{Total time} = \text{Number of descents} \times \text{Time per descent} = 18 \times 2 = 36 \, \text{minutes}
\]

4. **Conclusion:**
The fish will take **36 minutes** to reach a depth of -37.8 meters.

In summary, starting from -10.8 meters, it will take the fish 36 minutes to descend to -37.8 meters by swimming down 1.5 meters every 2 minutes.