solve the following word problem. A fish is swimming at −10.8

Question

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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
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37.8 meters? Show your work and write a sentence to explain what your answer means..

Answer 1

To solve the problem, we need to determine how many meters below sea level the fish needs to descend and how long it will take to reach that depth.

1. Determine the starting depth and target depth:

   • Starting depth = -10.8 meters
   • Target depth = -37.8 meters

2. Calculate the total depth to descend: \[ \text{Depth to descend} = \text{Target depth} - \text{Starting depth} = (-37.8) - (-10.8) \] \[ \text{Depth to descend} = -37.8 + 10.8 = -27.0 \text{ meters} \]

3. Determine the rate of descent:

   • The fish descends 1.5 meters every 2 minutes.

4. Calculate the time to descend 27.0 meters:

   • First, find out how many 1.5 meter descents are needed: \[ \text{Number of descents} = \frac{27.0 \text{ meters}}{1.5 \text{ meters/2 minutes}} = \frac{27.0}{1.5} = 18 \]

5. Calculate the total time:

   • Since each descent takes 2 minutes, the total time is: \[ \text{Total time} = 18 \text{ descents} \times 2 \text{ minutes/descent} = 36 \text{ minutes} \]

Final Answer: It will take the fish 36 minutes to reach a depth of -37.8 meters.

Explanation

This means that after swimming for 36 minutes, the fish will have descended from 10.8 meters below sea level to 37.8 meters below sea level.