Solve a multi-step real-world problem involving rational numbers.

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. 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.

Answer 1

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.