Question
A fish is swimming at -10.8 m below sea level every two minutes it to send 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 swimming at -10.8 m below sea level to reach a depth of -37.8 m, we can follow these steps:
1. **Calculate the total depth the fish needs to reach:**
- The fish starts at -10.8 m and needs to reach -37.8 m.
- To find the total distance to descend, we can subtract the starting depth from the target depth:
\[
\text{Total Depth} = -37.8 \, \text{m} - (-10.8 \, \text{m}) = -37.8 \, \text{m} + 10.8 \, \text{m} = -27.0 \, \text{m}
\]
2. **Calculate how much the fish descends every two minutes:**
- The fish swims down at a rate of 1.5 m every two minutes.
3. **Calculate the number of two-minute intervals needed to cover the total distance:**
- We need to find out how many two-minute intervals (let’s call this \( n \)) it takes to descend a total of -27.0 m. The formula for this is given by:
\[
n = \frac{\text{Total Depth}}{\text{Depth per Interval}} = \frac{-27.0 \, \text{m}}{-1.5 \, \text{m/2 min}} \rightarrow \text{(we drop the negative sign for calculation)}
\]
\[
n = \frac{27.0 \, \text{m}}{1.5 \, \text{m/2 min}} = \frac{27.0}{1.5} \times 2 = 18 \times 2 = 36 \, \text{minutes}
\]
4. **Determine the total time:**
- Since each interval is 2 minutes long, we multiply the number of intervals by 2:
\[
\text{Total Time} = n \cdot 2 \, \text{min} = 18 \times 2 \, \text{min} = 36 \, \text{min}
\]
Thus, it will take the fish **36 minutes** to reach a depth of -37.8 meters.
### Explanation
This means that if the fish continues to swim at a consistent rate of 1.5 meters every two minutes, it will take a total of 36 minutes for it to reach the desired depth of -37.8 meters below sea level from its starting point of -10.8 meters.
1. **Calculate the total depth the fish needs to reach:**
- The fish starts at -10.8 m and needs to reach -37.8 m.
- To find the total distance to descend, we can subtract the starting depth from the target depth:
\[
\text{Total Depth} = -37.8 \, \text{m} - (-10.8 \, \text{m}) = -37.8 \, \text{m} + 10.8 \, \text{m} = -27.0 \, \text{m}
\]
2. **Calculate how much the fish descends every two minutes:**
- The fish swims down at a rate of 1.5 m every two minutes.
3. **Calculate the number of two-minute intervals needed to cover the total distance:**
- We need to find out how many two-minute intervals (let’s call this \( n \)) it takes to descend a total of -27.0 m. The formula for this is given by:
\[
n = \frac{\text{Total Depth}}{\text{Depth per Interval}} = \frac{-27.0 \, \text{m}}{-1.5 \, \text{m/2 min}} \rightarrow \text{(we drop the negative sign for calculation)}
\]
\[
n = \frac{27.0 \, \text{m}}{1.5 \, \text{m/2 min}} = \frac{27.0}{1.5} \times 2 = 18 \times 2 = 36 \, \text{minutes}
\]
4. **Determine the total time:**
- Since each interval is 2 minutes long, we multiply the number of intervals by 2:
\[
\text{Total Time} = n \cdot 2 \, \text{min} = 18 \times 2 \, \text{min} = 36 \, \text{min}
\]
Thus, it will take the fish **36 minutes** to reach a depth of -37.8 meters.
### Explanation
This means that if the fish continues to swim at a consistent rate of 1.5 meters every two minutes, it will take a total of 36 minutes for it to reach the desired depth of -37.8 meters below sea level from its starting point of -10.8 meters.