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Solve the following word problem. A fish is swimming at −10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descen...Asked by p diddy
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.(4 points) The answer is clear and correct. The answer shows that the student used problem-solving skills and reasoning. All work is shown or explained.
Answers
Answered by
p diddy
make it with sentences in 4 sentences
Answered by
GPT-4o mini
To solve the problem, we need to find out how long it will take for the fish to reach a depth of −37.8 meters, starting from −10.8 meters and descending 1.5 meters every 2 minutes.
1. **Determine the total depth the fish needs to descend.**
Starting depth: -10.8 meters
Target depth: -37.8 meters
To find the total distance the fish needs to descend, we can subtract the starting depth from the target depth:
\[
\text{Total depth to descend} = \text{Target depth} - \text{Starting depth}
\]
\[
= -37.8 - (-10.8)
\]
\[
= -37.8 + 10.8
\]
\[
= -27.0 \text{ meters}
\]
This means the fish needs to descend 27.0 meters to reach -37.8 meters.
2. **Determine how many 2-minute intervals of descent are needed.**
The fish descends 1.5 meters every 2 minutes. To find out how many intervals of 1.5 meters are needed to descend 27.0 meters, we can divide the total descent by the distance per interval:
\[
\text{Number of intervals} = \frac{\text{Total depth to descend}}{\text{Depth per interval}}
\]
\[
= \frac{27.0 \text{ meters}}{1.5 \text{ meters/interval}}
\]
\[
= 18 \text{ intervals}
\]
3. **Convert intervals to time.**
Since each interval takes 2 minutes, we can find the total time taken by multiplying the number of intervals by the time per interval:
\[
\text{Total time} = \text{Number of intervals} \times \text{Time per interval}
\]
\[
= 18 \times 2 \text{ minutes}
\]
\[
= 36 \text{ minutes}
\]
**Answer: 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 below sea level, the fish will take 36 minutes to further descend to a depth of 37.8 meters below sea level.
1. **Determine the total depth the fish needs to descend.**
Starting depth: -10.8 meters
Target depth: -37.8 meters
To find the total distance the fish needs to descend, we can subtract the starting depth from the target depth:
\[
\text{Total depth to descend} = \text{Target depth} - \text{Starting depth}
\]
\[
= -37.8 - (-10.8)
\]
\[
= -37.8 + 10.8
\]
\[
= -27.0 \text{ meters}
\]
This means the fish needs to descend 27.0 meters to reach -37.8 meters.
2. **Determine how many 2-minute intervals of descent are needed.**
The fish descends 1.5 meters every 2 minutes. To find out how many intervals of 1.5 meters are needed to descend 27.0 meters, we can divide the total descent by the distance per interval:
\[
\text{Number of intervals} = \frac{\text{Total depth to descend}}{\text{Depth per interval}}
\]
\[
= \frac{27.0 \text{ meters}}{1.5 \text{ meters/interval}}
\]
\[
= 18 \text{ intervals}
\]
3. **Convert intervals to time.**
Since each interval takes 2 minutes, we can find the total time taken by multiplying the number of intervals by the time per interval:
\[
\text{Total time} = \text{Number of intervals} \times \text{Time per interval}
\]
\[
= 18 \times 2 \text{ minutes}
\]
\[
= 36 \text{ minutes}
\]
**Answer: 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 below sea level, the fish will take 36 minutes to further descend to a depth of 37.8 meters below sea level.
Answered by
GPT-4o mini
To determine how long it will take for the fish to reach a depth of -37.8 meters, we first calculate that it needs to descend a total of 27.0 meters, starting from -10.8 meters. The fish descends 1.5 meters every 2 minutes, which means it requires 18 intervals to cover the total distance. Since each interval lasts 2 minutes, we multiply the 18 intervals by 2 minutes, resulting in a total of 36 minutes. Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.