Question
Solve a multi-step real-world problem involving rational numbers.
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. 1. How long will it take for the fish to reach a depth of -37.8 meters? 2. Show your work and 3. write a sentence to explain what your answer means.
Answer: It will take 36 minutes for the fish to reach a depth of -37.8 meters.
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. 1. How long will it take for the fish to reach a depth of -37.8 meters? 2. Show your work and 3. write a sentence to explain what your answer means.
Answer: It will take 36 minutes for the fish to reach a depth of -37.8 meters.
Answers
GPT-4o mini
To solve this problem, we need to determine how long it will take for the fish to descend from -10.8 meters to -37.8 meters in depth.
1. **Determine the total depth the fish needs to descend:**
The starting depth of the fish is -10.8 meters, and it needs to reach -37.8 meters.
\[
\text{Total descent} = \text{final depth} - \text{initial depth}
\]
\[
\text{Total descent} = -37.8 - (-10.8)
\]
\[
\text{Total descent} = -37.8 + 10.8
\]
\[
\text{Total descent} = -27.0 \text{ meters}
\]
Therefore, the fish needs to descend 27 meters.
2. **Calculate how many 2-minute intervals are needed for the descent:**
The fish descends 1.5 meters every 2 minutes. To find out how many 2-minute intervals it takes to cover 27 meters, we can use the following formula:
\[
\text{Number of intervals} = \frac{\text{Total descent}}{\text{Descent per interval}}
\]
\[
\text{Number of intervals} = \frac{27.0}{1.5}
\]
\[
\text{Number of intervals} = 18
\]
3. **Calculate the total time taken:**
Since each interval is 2 minutes, we multiply the number of intervals by the duration of each interval:
\[
\text{Total time (in minutes)} = \text{Number of intervals} \times \text{Interval duration}
\]
\[
\text{Total time} = 18 \times 2 = 36 \text{ minutes}
\]
### Conclusion:
It will take **36 minutes** for the fish to reach a depth of -37.8 meters.
**Explanation:** This means that starting from a depth of -10.8 meters, the fish will take 36 minutes of swimming at a rate of 1.5 meters every 2 minutes to attain a depth of -37.8 meters in the water.
1. **Determine the total depth the fish needs to descend:**
The starting depth of the fish is -10.8 meters, and it needs to reach -37.8 meters.
\[
\text{Total descent} = \text{final depth} - \text{initial depth}
\]
\[
\text{Total descent} = -37.8 - (-10.8)
\]
\[
\text{Total descent} = -37.8 + 10.8
\]
\[
\text{Total descent} = -27.0 \text{ meters}
\]
Therefore, the fish needs to descend 27 meters.
2. **Calculate how many 2-minute intervals are needed for the descent:**
The fish descends 1.5 meters every 2 minutes. To find out how many 2-minute intervals it takes to cover 27 meters, we can use the following formula:
\[
\text{Number of intervals} = \frac{\text{Total descent}}{\text{Descent per interval}}
\]
\[
\text{Number of intervals} = \frac{27.0}{1.5}
\]
\[
\text{Number of intervals} = 18
\]
3. **Calculate the total time taken:**
Since each interval is 2 minutes, we multiply the number of intervals by the duration of each interval:
\[
\text{Total time (in minutes)} = \text{Number of intervals} \times \text{Interval duration}
\]
\[
\text{Total time} = 18 \times 2 = 36 \text{ minutes}
\]
### Conclusion:
It will take **36 minutes** for the fish to reach a depth of -37.8 meters.
**Explanation:** This means that starting from a depth of -10.8 meters, the fish will take 36 minutes of swimming at a rate of 1.5 meters every 2 minutes to attain a depth of -37.8 meters in the water.