Question
A fish is swimming at -10.8 m or 10.8 m below sea level. Every two minutes is distance another 1.5 m. How long will it take for the fish to reach a depth of -37.8 m show your work and write a sentence to explain what your answer means.
Answers
GPT-4o mini
To determine how long it will take for the fish to reach a depth of -37.8 m, we can follow these steps:
1. **Identify the Starting and Target Depths:**
- Current depth of the fish: \( -10.8 \, \text{m} \)
- Target depth of the fish: \( -37.8 \, \text{m} \)
2. **Calculate the Depth Increase Needed:**
\[
\text{Depth increase} = \text{Target depth} - \text{Current depth}
\]
\[
\text{Depth increase} = -37.8 \, \text{m} - (-10.8 \, \text{m}) = -37.8 + 10.8 = -27 \, \text{m}
\]
3. **Determine the Rate of Movement:**
- The fish moves downwards at a rate of 1.5 m every 2 minutes. Therefore, the rate in meters per minute is:
\[
\text{Rate} = \frac{1.5 \, \text{m}}{2 \, \text{min}} = 0.75 \, \text{m/min}
\]
4. **Calculate the Time Required to Reach Target Depth:**
- We need to find the time needed to cover -27 m at a rate of 0.75 m/min.
\[
\text{Time} = \frac{\text{Depth increase}}{\text{Rate}} = \frac{27 \, \text{m}}{0.75 \, \text{m/min}} = 36 \, \text{minutes}
\]
5. **Conclusion:**
- It will take the fish **36 minutes** to reach a depth of -37.8 m.
**Sentence Explanation**: The fish, currently swimming at -10.8 m below sea level, will take 36 minutes to reach a depth of -37.8 m by swimming at a speed of 1.5 m every 2 minutes.
1. **Identify the Starting and Target Depths:**
- Current depth of the fish: \( -10.8 \, \text{m} \)
- Target depth of the fish: \( -37.8 \, \text{m} \)
2. **Calculate the Depth Increase Needed:**
\[
\text{Depth increase} = \text{Target depth} - \text{Current depth}
\]
\[
\text{Depth increase} = -37.8 \, \text{m} - (-10.8 \, \text{m}) = -37.8 + 10.8 = -27 \, \text{m}
\]
3. **Determine the Rate of Movement:**
- The fish moves downwards at a rate of 1.5 m every 2 minutes. Therefore, the rate in meters per minute is:
\[
\text{Rate} = \frac{1.5 \, \text{m}}{2 \, \text{min}} = 0.75 \, \text{m/min}
\]
4. **Calculate the Time Required to Reach Target Depth:**
- We need to find the time needed to cover -27 m at a rate of 0.75 m/min.
\[
\text{Time} = \frac{\text{Depth increase}}{\text{Rate}} = \frac{27 \, \text{m}}{0.75 \, \text{m/min}} = 36 \, \text{minutes}
\]
5. **Conclusion:**
- It will take the fish **36 minutes** to reach a depth of -37.8 m.
**Sentence Explanation**: The fish, currently swimming at -10.8 m below sea level, will take 36 minutes to reach a depth of -37.8 m by swimming at a speed of 1.5 m every 2 minutes.